bluuebunny/crossref_metadata_2025 huggingface dataset:
On Nilpotent Extensions of Algebras
Authors: Marczak Adam W. , Płonka Jerzy
Published: February 2014

In this paper, we investigate essentially n-ary term operations of nilpotent extensions of algebras. We detect the connection between term operations of an original algebra and its nilpotent extensions. This structural point of view easily leads to the conclusion that the number of distinct essentially n-ary term operations of a proper algebraic nilpotent extension 𝔄 of an algebra ℑ is given by the formula [Formula: see text] We show that in general the converse theorem is not true. However, we suppose that if a variety [Formula: see text] is uniquely determined by its pn-sequences, the converse theorem is also satisfied. In the second part of the paper, we characterize generics of nilpotent shifts of varieties and describe cardinalities of minimal generics. We give a number of examples and pose some problems.
Linear Syzygies from k-Configurations in ℙn and the Mapping Cone Constructions
Authors: Shin Yong Su
Published: February 2014

We find a necessary and sufficient condition for the Hilbert function to support the ith linear syzygy using type vectors and also construct an Artinian level algebra whose minimal free resolution supports the nth linear syzygy using both a mapping cone construction and coordinate points in ℙn.
Several Diophantine Equations in Some Rings of Integers of Quadratic Imaginary Fields
Authors: Xu Kejian , Wang Yongliang
Published: February 2014

In this paper, it is proved that the Diophantine equation x4-y4 =z2 has no non-trivial coprime solutions in the rings of integers of quadratic imaginary fields [Formula: see text] for d=11, 19, 43, 67, 163, which implies that the Fermat equation x4+y4 =z4 has no non-trivial solutions in these fields either. Then all the solutions of the Pocklington equation x4-x2y2+y4 =(-1)σz2 (σ =0 or 1) in the ring of integers of [Formula: see text] are determined, and as an application, the result is applied to K2 of a field.
Abundant Semigroups with Q-adequate Transversals and Some of Their Special Cases
Authors: Guo Xiaojiang , Shum K. P.
Published: February 2014

Regular semigroups with multiplicative inverse transversals were first studied by Blyth and McFadden in 1982. In this paper, we extend the concept of inverse transversals to some kind of quasi-ideal adequate transversals of abundant semigroups. Some characterization theorems of abundant semigroups with different kinds of quasi-ideal adequate transversals are obtained. In particular, the structure theory of abundant semigroups having different kinds of quasi-ideal adequate transversals is established. Some results obtained by Blyth, McAlister and McFadden on inverse transversals in regular semigroups are hence extended to abundant semigroups.
Morphisms and Functor kerf in C-Algebras
Authors: Xu Bangteng
Published: February 2014

Let (A,B,f) be a C-algebra. For any subset N of B, its kernel ker fN is a subset of [Formula: see text]. The kernel ker f has been used to obtain important results for C-algebras (see [2] and [4]). In this paper, we study further properties of ker f. In particular, for a transitional C-algebra (A,B,f) and quotient subsets M and N such that N ⊆ M and M is also a C-subset, we prove that [Formula: see text]. In order to show this result, exact sequences in C-algebras are studied. Finally, we present a few examples and applications.
Menger Algebras and Clones of Cooperations
Authors: Denecke Klaus , Saengsura Kittisak
Published: February 2014

The superposition of cooperations satisfies the well-known clone axioms (C1), (C2) and (C3). We define terms for indexed coalgebras of type τ, cooperations induced by those terms, and prove that the set of all induced cooperations forms a clone. This clone is equal to the clone of all cooperations generated by the fundamental cooperations of an indexed coalgebra. Finally, we introduce the concept of rational equivalence for coalgebras and determine all two-element coalgebras up to rational equivalence.
Verma Modules over a Block Lie Algebra
Authors: Jiang Qifen , Wu Yuezhu
Published: February 2014

Let [Formula: see text] be the Lie algebra with basis {Li,j, C|i, j ∈ ℤ} and relations [Li,j, Lk,l] = ((j + 1)k - i(l + 1))Li+k, j+l + iδi, -kδj+l, -2C and [C, Li,j] = 0. It is proved that an irreducible highest weight [Formula: see text]-module is quasifinite if and only if it is a proper quotient of a Verma module. An additive subgroup Γ of 𝔽 corresponds to a Lie algebra [Formula: see text] of Block type. Given a total order ≻ on Γ and a weight Λ, a Verma [Formula: see text]-module M(Λ, ≻) is defined. The irreducibility of M(Λ, ≻) is completely determined.
A Theorem of Finite Groups with 18p Elements Having Maximal Order
Authors: Jiang Youyi
Published: February 2014

In this paper, we prove that for any prime p, a finite group with 18p elements having maximal order is solvable. This result provides some information in solving an open problem proposed by Thompson.
A Correction to “A Remark on the Green Correspondence on G-Algebras”
Authors: Harris Morton E.
Published: February 2014

This note presents a counterexample to [1, Proposition 1(d)] that was communicated by Külshammer. The proof of [1, Proposition 1(d)] is erroneous.
Prime Ideals in Group Near-rings
Authors: Groenewald N. J. , Juglal S. , Meyer J. H.
Published: February 2014

The flow (or lack thereof) of several kinds of primeness between a zero-symmetric near-ring R and its group near-ring R[G] for certain groups G is discussed. In certain cases, results are contrasted against what happens in the matrix near-ring situation.
Semilattices of Archimedean Ordered Semigroups
Authors: Kehayopulu Niovi , Tsingelis Michael
Published: February 2014

In this paper we deal with the decomposition of some classes of ordered semigroups into archimedean components. In particular, we prove that in ordered semigroups the concepts of semilattices of archimedean semigroups and of complete semilattices of archimedean semigroups are the same. In addition, we discuss similarities and differences between semigroups (without order) and ordered semigroups.
All Finite Generalized Tetrahedron Groups
Authors: Fine Benjamin , Hahn Miriam , Hulpke Alexander , große Rebel Volkmar , Rosenberger Gerhard , Scheer Martin
Published: February 2014

A generalized tetrahedron group is defined to be a group admitting a presentation [Formula: see text] where l, m, n, p, q, r ≥ 2, each Wi(a,b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized triangle groups. In this paper, we build on previous work to give a complete classification of all finite generalized tetrahedron groups.
Decomposition Theory of Perfect Modules
Authors: Wu Zhixiang , Shum K. P.
Published: February 2014

The decomposition theory of perfect modules is developed and consequently the decomposition of comodules is extended to perfect modules over an arbitrary ring. In addition, a decomposition theorem of finitely generated torsion modules over PID is established and the theory of Dickson on the primary decomposition of modules becomes a special case of our result.
Finiteness Results on Generalized Local Cohomology Modules
Authors: Zamani Naser
Published: February 2014

Let (R, 𝔪) be a local ring, 𝔞 an ideal of R, and M, N be two finitely generated R-modules. We show that r = gdepth (M/𝔞M, N) is the least integer such that [Formula: see text] has infinite support. Also, we prove that the first non-Artinian generalized local cohomology module has finitely many associated primes.
Graded Involutions on Upper-triangular Matrix Algebras
Authors: Valenti A. , Zaicev M. V.
Published: February 2014

Let UTn be the algebra of n × n upper-triangular matrices over an algebraically closed field of characteristic zero. We describe all G-gradings on UTn by a finite abelian group G commuting with an involution (involution gradings).
On the Finiteness Results of the Generalized Local Cohomology Modules
Authors: Mafi Amir
Published: February 2014

Let 𝔞 be an ideal of a commutative Noetherian local ring R, and let M and N be two finitely generated R-modules. Let t be a positive integer. It is shown that if the support of the generalized local cohomology module [Formula: see text] is finite for all i < t, then the set of associated prime ideals of the generalized local cohomology module [Formula: see text] is finite. Also, if the support of the local cohomology module [Formula: see text] is finite for all i < t, then the set [Formula: see text] is finite. Moreover, we prove that gdepth (𝔞+ Ann (M),N) is the least integer t such that the support of the generalized local cohomology module [Formula: see text] is an infinite set.
Products of Finite Supersoluble Groups
Authors: Liu Xi , Guo Wenbin , Shum K. P.
Published: February 2014

Let H and T be subgroups of a finite group G. We say that H is completely c-permutable with T in G if there exists an element x ∈ 〈H,T〉 such that HTx= TxH. In this paper, we use this concept to determine the supersolubility of a group G = AB, where A and B are supersoluble subgroups of G. Some criterions of supersolubility of such groups are obtained and some known results are generalized.
Commutative Zero-divisor Semigroups of Graphs with at Most Four Vertices
Authors: Tang Gaohua , Su Huadong , Ren Beishang
Published: February 2014

The zero-divisor graph of a commutative semigroup with zero is a graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices joined by an edge in case their product in the semigroup is zero. In this paper, we study commutative zero-divisor semigroups determined by graphs. We determine all corresponding zero-divisor semigroups of all simple graphs with at most four vertices.
On t-Dimension of Polynomial Rings
Authors: Wang Fanggui
Published: February 2014

In this paper, we study the t-dimension of a pullback and show that for any pair of integers (n,m) with 1 ≤ n ≤ m ≤ 2n-1, there is a domain R such that t- dim (R)=n and t- dim (R[X])=m.
On Conjugacy Class Sizes of the p′-Elements with Prime Power Order
Authors: Zhao Xianhe , Guo Xiuyun
Published: February 2014

In this paper we prove that a finite p-solvable group G is solvable if its every conjugacy class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every conjugacy class size of 2′-elements with prime power order.
On Certain Distinguished Involutions in the Weyl Group of Type Bn
Authors: Chen Chengdong , Liu Jiachun
Published: February 2014

Let (W,S) be a Weyl group of type Bn. In this paper, we find certain nontrivial distinguished involutions in the two-sided cell Ωt of W with a-value [Formula: see text] for 1≤ 2t ≤ n and n even (resp., [Formula: see text] for 1≤ 2t < n and n odd). Besides, for 1≤ i1< ⋯ < it≤ n-1, let Li1⋯ it be a left cell of W with a-value t2 and R(Li1⋯ it) ={si1,…,sit}. There are only two involutions y(i1,i1)⋯ y(it-1,it-1) sit and y(i1,i1)⋯ y(it,it) in the left cell Li1⋯ it. We prove that the former (resp., latter) is a distinguished involution in the left cell Li1⋯ it for t odd (resp., even).
Stationary Subsets of Functional Menger ∩-Algebras of Multiplace Functions
Authors: Dudek Wieslaw A. , Trokhimenko Valentin S.
Published: February 2014

A functional Menger ∩-algebra is a set of n-place functions containing n projections and closed under the so-called Menger's composition of n-place functions and the set-theoretic intersection of functions. We give the abstract characterization for these subsets of functional Menger ∩-algebras which contain functions with fixed points.
On Exchange Hermitian Rings
Authors: Chen Huanyin
Published: February 2014

In this article, we investigate new necessary and sufficient conditions on an exchange ring under which every regular matrix admits a diagonal reduction. We prove that an exchange ring R is an hermitian ring if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that x = xux; if and only if for any n ≥ 2 and any regular x ∈ Rn, there exists u ∈ CLn(R) such that xu ∈ R is an idempotent. Furthermore, we characterize such exchange rings by means of reflexive inverses and n-pseudo-similarity.
On Jordan Banach Algebras with Countably Generated Inner Ideals
Authors: Boudi Nadia
Published: February 2014

In this paper, we show that if J is a complex Jordan Banach algebra in which inner ideals are countably generated, then J is finite dimensional. We also study the real case.
On Rings Whose Strongly Prime Ideals Are Completely Prime
Authors: Huh Chan , Lee Chang Ik , Lee Yang
Published: February 2014

Kaplansky introduced the concept of the K-rings, concerning the commutativity of rings. In this paper, we concentrate on a property of K-rings, introducing the concept of the strongly NI rings, which is stronger than NI-ness. We first examine the relations among the concepts concerned with K-rings and strongly NI rings, constructing necessary examples in the process. We also show that strong NI-ness is a hereditary radical property.
The c-Normal Embedding Property in Finite Groups (I)
Authors: Wei Huaquan , Wang Yanming , Yang Liying
Published: February 2014

We introduce a new subgroup embedding property of finite groups called c-normal embedding. By using this embedding property, formation theory and some special techniques, we obtain `iff' versions of theorems of Itô, Buckley, Srinivasan and other related results on p-nilpotence, nilpotence and supersolvability.
A Universal Variety of Point Algebras
Authors: Padmanabhan R. , Penner P.
Published: February 2014

Point algebras introduced by Evans are algebraic systems which capture the essence of multiplications (a,b) · (c,d)=(p,q) defined on the set of all ordered pairs of elements of a set S, where p and q are selected from among a,b,c,d by some well-defined rule. In 1961, Jonsson and Tarski gave an interesting example of a variety of algebras of type 〈2,1,1〉 for illustrating the failure of certain free algebra properties. In this paper, we show that this equational class of algebras, called the JT-variety, is a universal variety of point algebras in the sense that every variety generated by a point algebra is a reduct of the JT-variety.
Singleton's Bound in Euclidean Codes
Authors: Jain Sapna
Published: February 2014

There are three standard weight functions on a linear code viz. the Hamming weight, Lee weight and Euclidean weight. The Euclidean weight function is useful in connection with the lattice constructions, where the minimum norm of vectors in the lattice is related to the minimum Euclidean weight of the code. In this paper, we obtain Singleton's bound for Euclidean codes and introduce maximum Euclidean square distance separable (MESDS) codes.
On the Largest Irreducible Character Degree of a Finite Solvable Group
Authors: Jafari M. H.
Published: February 2014

Let b(G) denote the largest irreducible character degree of a finite group G. In this paper, we prove that if G is a solvable group which does not involve a section isomorphic to the wreath product of two groups of equal prime order p, and if b(G) < pn, then |G:Op(G)|p < pn.
On Polynomial Graded Subalgebras of a Polynomial Algebra
Authors: Jędrzejewicz Piotr
Published: February 2014

Let k be a field of arbitrary characteristic and let k[x1,…,xn] be the polynomial k-algebra. We describe, in some special cases, polynomial graded subalgebras of k[x1,…,xn] containing [Formula: see text], where p is a prime number.
Ordinary Grothendieck Groups of a Frobenius P-Category
Authors: Puig Lluis
Published: February 2014

In [7] we have introduced the Frobenius categories [Formula: see text] over a finite p-group P, and we have associated to [Formula: see text] — suitably endowed with some central k*-extensions — a “Grothendieck group” as an inverse limit of Grothendieck groups of categories of modules in characteristic p obtained from [Formula: see text], determining its rank. Our purpose here is to introduce an analogous inverse limit of Grothendieck groups of categories of modules in characteristic zero obtained from [Formula: see text], determining its rank and proving that its extension to a field is canonically isomorphic to the direct sum of the corresponding extensions of the “Grothendieck groups” above associated with the centralizers in [Formula: see text] of a suitable set of representatives of the [Formula: see text]-classes of elements of P.
Obstructions to Lie–Rinehart Algebra Extensions
Authors: Casas J. M.
Published: February 2014

The problem of the representation of an action of a Lie–Rinehart algebra on a Lie 𝖠-algebra by means of a homomorphism of Lie–Rinehart algebras is studied. An eight-term exact sequence associated to an epimorphism of Lie–Rinehart algebras for the cohomology of Lie–Rinehart algebras developed by Casas, Ladra and Pirashvili is obtained. This sequence is applied to study the obstruction theory of Lie–Rinehart algebra extensions.
Another Uniqueness Proof of the Dickson Simple Group G2(3)
Authors: Michler Gerhard O. , Wang Lizhong
Published: February 2014

In this article, we give a self-contained uniqueness proof for the Dickson simple group G=G2(3) using the first author's uniqueness criterion. The uniqueness proof for G2(3) was first given by Janko. His proof depends on Thompson's deep and technical characterization of G2(3).

Let H′ be the amalgamated central product of SL 2(3) with itself. Then there is a unique extension H of H′ by a cyclic group of order 2 such that H has a center of order 2 and both factors SL 2(3) are normal in H. We prove that any simple group G having a 2-central involution z with centralizer CG(z)≅ H is isomorphic to G2(3).
On a Problem of Brešar
Authors: Wang Yu
Published: February 2014

The main purpose of this paper is to investigate an additive range-inclusive map from a semiprime ring with idempotents into its maximal right quotient ring. As a corollary to our main result we obtain a simple proof of a result by Brešar. Our approach is based on connecting range-inclusive maps with the theories of local derivations and biderivations.
Automorphism Groups of the Imprimitive Complex Reflection Groups II
Authors: Wang Li
Published: February 2014

We prove that the automorphism group Aut (m,p,n) of an imprimitive complex reflection group G(m,p,n) is the product of a normal subgroup T(m,p,n) by a subgroup R(m,p,n), where R(m,p,n) is the group of automorphisms that preserve reflections and T(m,p,n) consists of automorphisms that map every element of G(m,p,n) to a scalar multiple of itself.
Characterization of Aut(J2) and Aut(McL) by Their Non-commuting Graphs
Authors: Wang Lingli , Shi Wujie
Published: February 2014

For a non-abelian group G, we associate the non-commuting graph ∇ (G) whose vertex set is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. In this paper, we prove that Aut (J2) and Aut (McL) are characterized by their non-commuting graphs.
Automorphisms and p-Characters of Restricted Lie Superalgebras of Cartan Type
Authors: Yuan Jixia , Chen Yan , Liu Wende
Published: February 2014

Let X be a restricted Lie superalgebra of Cartan type W, S, H or K over a field of prime characteristic. In this paper, we describe the quotients of the standard normal series of the automorphism group of X. As an application, the results above are used to discuss the p-characters of the irreducible representations for X.
On Covers of Perfect Lie Algebras
Authors: Salemkar Ali Reza , Edalatzadeh Behrouz , Mohammadzadeh Hamid
Published: February 2014

A Lie algebra is said to be perfect when it coincides with its derived subalgebra. The paper is devoted to give a complete structure of covers of perfect Lie algebras. Also, similar to a result of Alperin and Gorenstein (1966) in group theory, it is shown that every automorphism of a finite dimensional perfect Lie algebra may be lifted to an automorphism of its cover. Moreover, we present the concepts of irreducible and primitive extensions of an arbitrary Lie algebra and give some equivalent conditions for a central extension to be irreducible or primitive. Finally, we study the connection between the primitive extensions and the stem covers of finite dimensional perfect Lie algebras.
A Characterization of l-Ideals in l-Groups
Authors: Yang Yichuan , Liu Liqiong
Published: February 2014

We present a characterization of l-ideals in an arbitrary l-group without use of inequalities, which generalizes the corresponding result of Alpay, Emel'yanov and Ercan for o-ideals in Riesz spaces.
Rees Modules and Reduction of an Ideal Relative to a Noetherian Module
Authors: Zamani Naser
Published: February 2014

Let (A, 𝔪) be a Noetherian local ring, E a non-zero finitely generated A-module, and 𝔟 a proper ideal of A. The aim of this paper is, under some assumptions on𝔟 and E, to clarify a necessary and sufficient condition for the Rees module of E associated to 𝔟 to obtain Cohen-Macaulayness. Also, among other independent results about the reduction number of 𝔟 relative to E, we expand a theorem of Marley.
Lie Triple Derivations on Triangular Matrices
Authors: Benkovič Dominik
Published: February 2014

Let [Formula: see text] be the algebra of all n × n upper triangular matrices over a commutative unital ring [Formula: see text], and let [Formula: see text] be a 2-torsion free unital [Formula: see text]-bimodule. We show that every Lie triple derivation [Formula: see text] is a sum of a standard Lie derivation and an antiderivation.
Symmetric Symplectic Commutative Associative Algebras and Related Lie Algebras
Authors: Baklouti Amir , Benayadi Saïd
Published: February 2014

A commutative associative algebra [Formula: see text] is called symmetric symplectic if it is endowed with both an associative non-degenerate symmetric bilinear form B and an invertible B-antisymmetric derivation D. We give a description of the commutative associative symmetric symplectic 𝕂-algebras by using the notion of T*-extension. Next, we introduce the notion of double extension of symmetric symplectic commutative associative algebras in order to give an inductive description of these algebras. Moreover, much information on the structure of symmetric commutative associative algebras is given in this paper.
Irreducible Representations of the Generalized Jacobson-Witt Algebras
Authors: Shu Bin , Yao Yufeng
Published: February 2014

Let L be the generalized Jacobson-Witt algebra W(m;n) over an algebraically closed field F of characteristic p > 3, which consists of special derivations on the divided power algebra R= 𝔄(m;n). Then L is a so-called generalized restricted Lie algebra. In such a setting, we can reformulate the description of simple modules of L with the generalized p-character χ when ht (χ) < min {pni-pni-1| 1 ≤ i ≤ m} for n=(n1,…,nm), which was obtained by Skryabin. This is done by introducing a modified induced module structure and thereby endowing it with a so-called (R,L)-module structure in the generalized χ-reduced module category, which enables us to apply Skryabin's argument to our case. Simple exceptional-weight modules are precisely constructed via a complex of modified induced modules, and their dimensions are also obtained. The results for type W are extended to the ones for types S and H.
A Characterization of Some Finite Simple Groups Through Their Orders and Degree Patterns
Authors: Akbari M. , Moghaddamfar A. R. , Rahbariyan S.
Published: February 2014

The degree pattern of a finite group G was introduced in [15] and denoted by D (G). A finite group M is said to be OD-characterizable if G ≅ M for every finite group G such that |G|=|M| and D (G)= D (M). In this article, we show that the linear groups Lp(2) and Lp+1(2) are OD-characterizable, where 2p-1 is a Mersenne prime. For example, the linear groups L2(2) ≅ S3, L3(2) ≅ L2(7), L4(2) ≅ A8, L5(2), L6(2), L7(2), L8(2), L13(2), L14(2), L17(2), L18(2), L19(2), L20(2), L31(2), L32(2), L61(2), L62(2), L89(2), L90(2), etc., are OD-characterizable. We also show that the simple groups L4(5), L4(7) and U4(7) are OD-characterizable.
The Character Correspondences on π-Separable Groups
Authors: Si Huabin , Zeng Jiwen
Published: February 2014

In this paper, we mainly consider the relationship between the complex irreducible characters of a π-separable group and the complex irreducible characters of its Hall π-subgroup. If a π-group S acts on a π-separable group G, let H be an S-invariant Hall π-subgroup of G and CNG(H)/H(S)=1. Then we construct a natural bijection from the set Lin S(H) onto the set Irr π′,S(G). Furthermore, we get a bijection from the linear characters of H onto Irr π′(G).
Quantum Weyl Polynomials and the Center of the Quantum Group Uq(𝔰𝔩3)
Authors: Li Libin , Wu Jingyan , Zhu Meiling
Published: February 2014

In this paper, we show that the center of the quantum group Uq(𝔰𝔩3) is the subalgebra of Uq(𝔰𝔩3) generated by three elements, and isomorphic to a quotient algebra of the polynomial algebra with three variables and one relation.
Elementary Superalgebras
Authors: Hou Bo , Yang Shilin
Published: February 2014

Let Λ be a finite-dimensional superalgebra over a field K. A characterization of an elementary superalgebra Λ is given by a quiver and a weight function. It is shown that Λ is elementary if and only if its Hochschild extension is elementary. Furthermore, if Λ is elementary of finite global dimension and {e1, …, en} is a complete set of gr-primitive orthogonal idempotents of Λ, then the following equalities hold: [Formula: see text] where ΦΛ is the Coxeter matrix of Λ, tr is the trace function of a matrix, HHi(Λ) and HHi(Λ) are the i-th Hochschild homology and cohomology, respectively.
On X-Permutable Subgroups
Authors: Li Baojun , Zhang Zhirang
Published: February 2014

A subgroup A of a group G is said to be X-permutable with another subgroup B in G, where ∅ ≠ X ⊆ G, if there exists some element x ∈ X such that ABx=BxA. In this paper, the solubility and supersolubility of finite groups are described by X-permutability of the Hall subgroups and their subgroups, in addition, the well known theorem of Schur-Zassenhaus in finite group is generalized.
Central Extensions and Derivations of Generalized Schrödinger-Virasoro Algebras
Authors: Wang Wei , Li Junbo , Xin Bin
Published: February 2014

Let 𝔽 be a field of characteristic 0, G an additive subgroup of 𝔽, s ∈ 𝔽 such that s ∉ G and 2s ∈ G. A class of infinite-dimensional Lie algebras [Formula: see text] called generalized Schrödinger-Virasoro algebras was defined by Tan and Zhang, which is a natural generalization of Schrödinger-Virasoro algebras. In this paper, central extensions and derivations of [Formula: see text] are determined.
A Combinatorial Approach to Specht Module Cohomology
Authors: Hemmer David J.
Published: February 2014

For a Specht module Sλ for the symmetric group Σd, the cohomology H i(Σd,Sλ) is known only in degree i = 0. We give a combinatorial criterion equivalent to the nonvanishing of the degree i = 1 cohomology, valid in odd characteristic. Our condition generalizes James' solution in degree zero. We apply this combinatorial description to give some computations of Specht module cohomology, together with an explicit description of the corresponding modules. Finally, we suggest some general conjectures that might be particularly amenable to proof using this description.
Determinantal Representation of Outer Inverses in Riemannian Space
Authors: Stanimirović Predrag S. , Zlatanović Milan Lj.
Published: February 2014

Starting from a known determinantal representation of outer inverses, we derive their determinantal representation in terms of the inner product in the Euclidean space. We define the double inner product of two miscellaneous tensors of rank 2 in a Riemannian space. The corresponding determinantal representation as well as the general representation of outer inverses in the Riemannian space are derived. A non-zero {2}-inverse X of a given tensor A obeying ρ(X) = s with 1 ≤ s ≤ r = ρ(A) is expressed in terms of the double inner product involving compound tensors with minors of order s, extracted from A and appropriate tensors.
On 2-Absorbing Submodules
Authors: Payrovi Sh. , Babaei S.
Published: February 2014

In this paper, we introduce the concept of 2-absorbing submodules as a generalization of 2-absorbing ideals. Let R be a commutative ring and M an R-module. A proper submodule N of M is called 2-absorbing if whenever a, b ∈ R, m ∈ M and abm ∈ N, then am ∈ N or bm ∈ N or ab ∈ N:RM. Let N be a 2-absorbing submodule of M. It is shown that N:RM is a 2-absorbing ideal of R and either Ass R(M/N) is a totally ordered set or Ass R(M/N) is the union of two totally ordered sets. Furthermore, it is shown that if M is a finitely generated multiplication module over a Noetherian ring R, and Ass R(M/N) a totally ordered set, then N is 2-absorbing whenever N:RM is a 2-absorbing ideal of R. Also, the 2-absorbing avoidance theorem is proved.
Symmetric Elements of Nonlinear Involutions in Group Rings
Authors: García-Delgado R. , Raposo A. P.
Published: February 2014

Given an involution φ : G → G in a group G and a ring R, we study the extensions, not necessarily linear, to an involution ψ : RG → RG in the group ring RG. We investigate the symmetric elements, those α ∈ RG for which ψ(α) = α, and give necessary and sufficient conditions for the set of symmetric elements, (RG)ψ, to be a subring of RG. This work is a generalization of [6] and references therein where only linear extensions of the group involution are considered.
Trace forms of Symbol Algebras
Authors: Flatley Ronan
Published: February 2014

Let S be a symbol algebra. The trace form of S is computed and it is shown how this form can be used to determine whether S is a division algebra or not. In addition, the exterior powers of the trace form of S are computed.
The Pairs of Finite p-Groups
Authors: Moghaddam Mohammad Reza R. , Salemkar Ali Reza , Davarpanah M.
Published: February 2014

Let M be a normal subgroup of a finite group G such that |G/M| = pm and |M/Z(M,G)| = pn. In this paper, we characterize all the pairs of groups (M,G) which satisfy the conditions [Formula: see text] and |[M/Z(M,G),G/Z(M,G)]|≤ p. If M has a complement in G and |M|=pn and |G/M|=pm, then there always exists a non-negative integer t(M,G) such that [Formula: see text]. Under some conditions, we determine all the pairs (M,G) with t(M,G)=0, 1 or 2.
Comparison of Multiplicity and Final Betti Number of a Standard Graded K-Algebra
Authors: Sahandi P. , Shirmohammadi N. , Yassemi S.
Published: February 2014

Let S be a polynomial ring over a field K and let R be the Stanley-Reisner ring of a matroid complex. In this paper, as a comparison of multiplicity and final Betti number of R over S, the inequality [Formula: see text] is obtained.
Finite Groups Whose Character Degree Graphs Are Empty Graphs
Authors: Meng Qingyun , Zeng Jiwen
Published: February 2014

In this paper, we classify and determine the structure of finite groups whose character degree graphs are empty graphs.
Finite Repetitive Generalized Cluster Complexes and d-Cluster Categories
Authors: Zou Teng , Zhu Bin
Published: February 2014

For any positive integer n, we construct an n-repetitive generalized cluster complex (a simplicial complex) associated with a given finite root system by defining a compatibility degree on the n-repetitive set of the colored root system. This simplicial complex includes Fomin-Reading's generalized cluster complex as a special case when n=1. We also introduce the intermediate coverings (called generalized d-cluster categories) of d-cluster categories of hereditary algebras, and study the d-cluster tilting objects and their endomorphism algebras in those categories. In particular, we show that the endomorphism algebras of d-cluster tilting objects in the generalized d-cluster categories provide the (finite) coverings of the corresponding (usual) d-cluster tilted algebras. Moreover, we prove that the generalized d-cluster categories of hereditary algebras of finite representation type provide a category model for the n-repetitive generalized cluster complexes.
On an Open Problem of Hereditary Property of Green's $\mathcal{H}$-Relation on Compact Semigroups
Authors: Guo Xiaojiang , Shum K. P.
Published: February 2014

We give a negative answer to an open problem concerning the hereditary property of Green's [Formula: see text]-relation on a compact semigroup proposed by Carruth and Clark in 1972. In addition, we give a positive answer to this open problem by adding some suitable conditions on the compact semigroup.
Generalized Derivations Having the Same Power Values with Left Multiplications
Authors: Xu Xiaowei , Ma Jing , Niu Fengwen
Published: February 2014

Let R be a prime ring with extended centroid C, maximal right ring of quotients U, a nonzero ideal I and a generalized derivation δ. Suppose δ(x)n =(ax)n for all x ∈ I, where a ∈ U and n is a fixed positive integer. Then δ(x)=λax for some λ ∈ C. We also prove two generalized versions by replacing I with a nonzero left ideal [Formula: see text] and a noncommutative Lie ideal L, respectively.
Generalized Inverse of Upper Triangular Infinite Dimensional Hamiltonian Operators
Authors: Huang Junjie , Guo Xiang , Huang Yonggang , Alatancang
Published: February 2014

In this paper, we deal with the generalized inverse of upper triangular infinite dimensional Hamiltonian operators. Based on the structure operator matrix J in infinite dimensional symplectic spaces, it is shown that the generalized inverse of an infinite dimensional Hamiltonian operator is also Hamiltonian. Further, using the decomposition of spaces, an upper triangular Hamiltonian operator can be written as a new operator matrix of order 3, and then an explicit expression of the generalized inverse is given.
Note on Lattice-ordered Rings with Positive Squares
Authors: Sun Yujiao , Yang Yichuan
Published: February 2014

Bourbaki, Birkhoff-Pierce and Fuchs pointed out or showed that a lattice-ordered field in which each square is positive must be totally ordered. Yang proved that a lattice-ordered ring R is a totally ordered skew-field if and only if every strictly positive element of R is invertible and each square in R is positive. In this note, we construct a simple example to explain the difference between order-isomorphisms and lattice-isomorphisms, and show that the difference can be dropped in lattice-ordered rings. Especially, this yields an extension and an elementary proof of the main theorem in Yang's paper.
Direct Products of Association Schemes and Tensor Products of Table Algebras
Authors: Xu Bangteng
Published: February 2014

In this paper we prove the Krull-Schmidt type theorems for direct products of association schemes and tensor products of table algebras.
Adjacency Matrices of PSL(2,5) and Resemblance of Its Coset Diagrams with Fullerene C60
Authors: Mushtaq Qaiser , Rafiq Ayesha
Published: February 2014

The action of PSL(2,ℤ) on PL(F5n) yields PSL(2,5). In this paper, we use the adjacency matrices of the abstract group PSL(2,5), eventually of fullerene C60, to draw the coset diagram and investigate various properties of the diagram with reference to the intransitivity of the action and the number of orbits.
Co-commutators with Generalized Derivations on Lie Ideals in Prime Rings
Authors: Dhara Basudeb
Published: February 2014

Let R be a prime ring of characteristic different from 2, L a noncentral Lie ideal of R, H and G two nonzero generalized derivations of R. Suppose us(H(u)u-uG(u)) ut=0 for all u ∈ L, where s, t ≥ 0 are fixed integers. Then either (i) there exists p ∈ U such that H(x)=xp for all x ∈ R and G(x)=px for all x ∈ R unless R satisfies S4, the standard identity in four variables; or (ii) R satisfies S4 and there exist p, q ∈ U such that H(x)=px+xq for all x ∈ R and G(x)=qx+xp for all x ∈ R.
Annihilator Conditions with Generalized Derivations on Multilinear Polynomials
Authors: Du Yiqiu , Wang Yu
Published: February 2014

Let R be a prime ring of characteristic different from 2 with right Utumi quotient ring U and extended centroid C. Let g be a generalized derivation of R, f(x1,…,xn) a multilinear polynomial over C, a ∈ R, and I a nonzero right ideal of R. Suppose that a[g(f(r1,…,rn)), f(r1,…,rn)]=0 for all ri∈ I and aI ≠ 0. Then either g(x)=a1x with (a1-γ)I=0 for some a1∈ U and γ ∈ C, or there exists an idempotent element e ∈ soc (RC) such that IC=eRC and one of the following holds: (i) f(x1,…,xn) is central-valued in eRe; (ii) g(x)=bx+xc, where b, c ∈ U with (c-b-α)e=0 for some α ∈ C and f(x1,…,xn) is central-valued in eRe.
Groups with Finiteness Conditions on the Lower Central Series of Subgroups
Authors: Rinauro Silvana
Published: February 2014

Let k be a positive integer. Locally graded groups G for which one of the sets {γk(H)| H ≤ G} and {γk(H)| H ≤G, H infinite } is finite are classified.
From orogen to passive margin: constraints from fission track and (U–Th)/He analyses on Mesozoic uplift and fault reactivation in SW Norway
Authors: Ksienzyk Anna K. , Dunkl István , Jacobs Joachim , Fossen Haakon , Kohlmann Fabian
Published: February 2014

The post-Caledonian tectonic history and landscape evolution of southwestern Norway are poorly understood, primarily owing to the lack of onshore post-Devonian sediments. To bridge this knowledge gap, low-temperature thermochronological techniques were applied to investigate vertical movements in the upper crust. New apatite fission track and apatite and zircon (U–Th)/He analyses on samples from southwestern Norway yielded Permian to Jurassic, Triassic to Cretaceous and Carboniferous to Triassic ages, respectively. Thermal history modelling indicates relatively high cooling rates (2–3 °C Ma
−1
) throughout Permian to early Jurassic times. Since the Jurassic, samples from coastal areas have remained close to the surface and were reheated to 30–50 °C during sedimentary burial in the Cretaceous. Inland samples experienced lesser amounts of Permo-Triassic exhumation, continued to cool slowly (<1 °C Ma
−1
) throughout the Jurassic–Cretaceous and did not reach the surface until the Cenozoic. Both fission track and (U–Th)/He ages are offset across faults, highlighting the importance of fault activity throughout the Mesozoic. In combination with previously published results, the new data suggest that the geomorphological evolution of southwestern Norway is closely connected to rift- and post-rift tectonics related to North Sea and North Atlantic rifting. The topographic relief was most likely repeatedly rejuvenated during periods of tectonic activity.
Why Did an Out-of-Hospital Shift of Death and Dying Occur in Canada after 1994?
Authors: Wilson Donna M. , Hewitt Jessica A. , Thomas Roger E. , Woytowich Boris
Published: February 2014

Canadian population mortality data reveal a significantly reduced proportion of deaths occurring in hospitals after 1994. Hospital deaths peaked at 80.5% in 1994, after a longstanding hospitalization-of-death trend in Canada. A decline in hospital-based death and dying has also occurred in some other countries. As the place of death can have multiple significant direct and indirect impacts on dying individuals, their families, and health services utilization and costs, it is important to understand factors for an out-of-hospital shift. An integrative review of Canadian print literature from 1995 was undertaken to identify these factors, with three themes emerging: (1) changes in health care and health system reforms after 1994 reduced both the availability and desirability of hospital-based care, (2) sociodemographic developments including aging of the population, increased multiculturalism, and diversity in accepted end-of-life care practices shifted place preferences, and (3) advances in palliative and end-of-life care, including a palliative care expansion out of hospital, supported nonhospital death, and dying processes. The period following 1994 was thus a time of major transformation during which the place of death and dying underwent important changes that supported and promoted a transition from hospital-based end-of-life care.
Validation of Factors Affecting the Outcome of Cardiopulmonary Arrest in a Large, Urban, Academic Medical Center
Authors: Koldobskiy Dafna , Groves Soleyah , Scharf Steven M. , Cowan Mark J.
Published: February 2014

Background. Recent studies of risks in cardiopulmonary arrest (CPA) have been performed using large databases from a broad mix of hospital settings. However, these risks might be different in a large, urban, academic medical center. We attempted to validate factors influencing outcomes from CPA at the University of Maryland Medical Center (UMMC). Methods. Retrospective chart review of all adult patients who underwent CPA between 2000 and 2005 at UMMC. Risk factors and outcomes were analyzed with appropriate statistical analysis and compared with published results. Results. 729 episodes of CPA were examined during the study period. Surgical patients had better survival than medical or cardiac patients. Intensive care unit' (ICU) patients had poor survival, but there was no difference on monitored or unmonitored floors. Respiratory etiologies survived better than cardiac etiologies. CPR duration and obesity were negatively correlated with outcome, while neurologic disease, trauma, and electrolyte imbalances improved survival. Age, gender, race, presence of a witness, presence of a monitor, comorbidities, or time of day of CPA did not influence survival, although age was associated with differences in comorbidities. Conclusions. UMMC risk factors for CPA survival differed from those in more broad-based studies. Care should be used when applying the results of database studies to specific medical institutions.
Pharmacodynamics of TRPV1 Agonists in a Bioassay Using Human PC-3 Cells
Authors: Alvarez-Berdugo Daniel , Jiménez Marcel , Clavé Pere , Rofes Laia
Published: February 2014

Purpose. TRPV1 is a multimodal channel mainly expressed in sensory neurons. We aimed to explore the pharmacodynamics of the TRPV1 agonists, capsaicin, natural capsaicinoids, and piperine in anin vitrobioassay using human PC-3 cells and to examine desensitization and the effect of the specific antagonist SB366791.Methods. PC-3 cells expressing TRPV1 were incubated with Fluo-4. Fluorescence emission changes following exposition to agonists with and without preincubation with antagonists were assessed and referred to maximal fluorescence following the addition of ionomycin. Concentration-response curves were fitted to the Hill equation.Results. Capsaicin and piperine had similar pharmacodynamics (Emax204.8 ± 184.3% piperine versus 176.6 ± 35.83% capsaicin,P=0.8814, Hill coefficient 0.70 ± 0.50 piperine versus 1.59 ± 0.86 capsaicin,P=0.3752). In contrast, capsaicinoids had lowerEmax(40.99 ± 6.14% capsaicinoids versus 176.6 ± 35.83% capsaicin,P<0.001). All the TRPV1 agonists showed significant desensitization after the second exposition and their effects were strongly inhibited by SB366791.Conclusion. TRPV1 receptor is successfully stimulated by capsaicin, piperine, and natural capsaicinoids. These agonists present desensitization and their effect is significantly reduced by a TRPV1-specific antagonist. In addition, PC-3 cell bioassays proved useful in the study of TRPV1 pharmacodynamics.
Adipocytes from New Zealand Obese Mice Exhibit Aberrant Proinflammatory Reactivity to the Stress Signal Heat Shock Protein 60
Authors: Märker Tina , Kriebel Jennifer , Wohlrab Ulrike , Burkart Volker , Habich Christiane
Published: February 2014

Adipocytes release immune mediators that contribute to diabetes-associated inflammatory processes. As the stress protein heat shock protein 60 (Hsp60) induces proinflammatory adipocyte activities, we hypothesized that adipocytes of diabetes-predisposed mice exhibit an increased proinflammatory reactivity to Hsp60. Preadipocytes and mature adipocytes from nonobese diabetic (NOD), New Zealand obese (NZO), and C57BL/6J mice were analyzed for Hsp60 binding, Hsp60-activated signaling pathways, and Hsp60-induced release of the chemokine CXCL-1 (KC), interleukin 6 (IL-6), and macrophage chemoattractant protein-1 (MCP-1). Hsp60 showed specific binding to (pre-)adipocytes of NOD, NZO, and C57BL/6J mice. Hsp60 binding involved conserved binding structure(s) and Hsp60 epitopes and was strongest to NZO mouse-derived mature adipocytes. Hsp60 exposure induced KC, IL-6, and MCP-1 release from (pre-)adipocytes of all mouse strains with a pronounced increase of IL-6 release from NZO mouse-derived adipocytes. Compared to NOD and C57BL/6J mouse derived cells, Hsp60-induced formation of IL-6, KC, and MCP-1 from NZO mouse-derived (pre-)adipocytes strongly depended on NFκB-activation. Increased Hsp60 binding and Hsp60-induced IL-6 release by mature adipocytes of NZO mice suggest that enhanced adipocyte reactivity to the stress signal Hsp60 contributes to inflammatory processes underlying diabetes associated with obesity and insulin resistance.
Acute Renal Failure after Consumption of Fish Gall Bladder
Authors: Pandey Nishant Raj , Yu Yao Bian , Khakurel Sudha
Published: February 2014

A case of acute renal failure after consumption of fish gall bladder as traditional medical remedy is reported. The patient fully recovered with conservative treatment. The risk of acute kidney failure and even multiple organ dysfunction syndrome following ingestion of fish gall bladder is highlighted.
Evaluation of Different Culture Media for Improvement in Bioinsecticides Production by IndigenousBacillus thuringiensisand Their Application against Larvae ofAedes aegypti
Authors: Devidas Patil Chandrashekhar , Pandit Borase Hemant , Vitthalrao Patil Satish
Published: February 2014

Production of indigenous isolateBacillus thuringiensissv2(Btsv2) was checked on conventional and nonconventional carbon and nitrogen sources in shake flasks. The effects on the production of biomass, toxin production, and spore formation capability of mosquito toxic strain were determined. Toxicity differs within the same strain depending on the growth medium.Btsv2produced with pigeon pea and soya bean flour were found highly effective withLC50<4 ppm against larvae ofAedes aegypti. These results were comparable with bacteria produced from Luria broth as a reference medium. Cost-effective analyses have revealed that production of biopesticide from test media is highly economical. The cost of production ofBtsv2with soya bean flour was significantly reduced by 23-fold. The use of nonconventional sources has yielded a new knowledge in this area as the process development aspects of biomass production have been neglected as an area of research. These studies are very important from the point of media optimization for economic production ofBacillus thuringiensisbased insecticides in mosquito control programmes.
Biomechanical Comparison of Different External Fixation Configurations for Posttraumatic Pelvic Ring Instability
Authors: Tiziani Simon , Osterhoff Georg , Ferguson Stephen J. , Spreiter Gregor , Scheyerer Max J. , Spinas Gian-Leza , Wanner Guido A. , Simmen Hans-Peter , Werner Clément M. L.
Published: February 2014

Background. External fixation is useful in the primary treatment of pelvic ring injuries. The present study compared the biomechanical stability of five different configurations of an external pelvic ring fixation system. Methods. Five configurations of an anterior external pelvic ring fixation system were tested using a universal testing machine. One single connecting rod was used in group “SINGLE,” two parallel connecting rods in group “DOUBLE,” two and four rods, respectively, in a tent-like configuration in groups “SINGLE TENT” and “DOUBLE TENT,” and a rhomboid-like configuration in group “RHOMBOID.” Each specimen was subjected to a total of 2000 consecutive cyclic loadings at 1 Hz lateral compression/distraction (±50 N) and torque (±0.5 Nm) loading alternating every 200 cycles. Translational and rotational stiffness were determined at 100, 300, 500, 700, and 900 cycles. Results. The “SINGLE TENT” and “RHOMBOID” configurations already failed with a preloading of 50 N compression force. The “DOUBLE” configuration had around twice the translational stability compared with the “SINGLE” and “DOUBLE TENT” configurations. Rotational stiffness observed for the “DOUBLE” and “DOUBLE TENT” configurations was about 50% higher compared to the SINGLE configuration. Conclusion. Using two parallel connecting rods provides the highest translational and rotational stability.