bluuebunny/crossref_metadata_2025 huggingface dataset:
Subnormal Inductive Sources and π-Partial Characters
Authors: Lewis Mark L.
Published: February 2014

A character pair (H,θ) in a group G consists of a subgroup H and a character θ ∈ Irr (H). A character pair (H,θ) is an inductive source in G if induction to G defines an injective map from the irreducible characters of T, the stabilizer of (H,θ), that lie over θ into Irr (G). Let π be a set of primes, and suppose G is π-separable. We consider Isaacs' π-partial characters and their canonical lifts. If θ ∈ Irr (H) is such a lift, then the restriction θ0 of θ to the π-elements of H is an irreducible π-partial character of H. In this paper, when (H,θ) is an inductive source so that H is subnormal and θ is a canonical lift, we show that induction is an injection from the irreducible π-partial characters of T that lie over θ0 to the irreducible π-partial characters of G. We apply this to obtain a partial generalization of Isaacs' nucleus of a character, and present several examples to see what can go wrong with our generalization.
Integrable Representations for Twisted Generalized Virasoro-Toroidal Lie Algebras
Authors: Fu Jiayuan , Jiang Cuipo , Su Yucai
Published: February 2014

In this paper, we classify irreducible integrable modules of twisted generalized Virasoro-toroidal Lie algebras τ with finite-dimensional weight spaces.
Grothendieck Groups of a Class of Quantum Doubles
Authors: Zhang Yun , Wu Feng , Liu Ling , Chen Hui-Xiang
Published: February 2014

Let k be a field and An(ω) be the Taft n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. We have constructed an n4-dimensional Hopf algebra Hn(p,q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω-1, and studied the irreducible and finite-dimensional representations of Hn(1,q). In this paper, we continue our study of Hn(1,q), examine the Grothendieck group G0(Hn(1,q)) ≅ G0(D(An(ω)), and describe its ring structure. We also give the Loewy length of the tensor product of two simple modules over Hn(1,q).
Matrices with Prescribed Eigenvalues and Blocks, II
Authors: Cravo Glória
Published: February 2014

Let F be a field and let n, p1, p2, p3 be positive integers such that n=p1+p2+p3. Let [Formula: see text] where the blocks Ci,j are of type pi× pj (i, j∈ {1,2,3}) and C1,1, C2,2, C3,3 are square submatrices. In this paper we describe conditions for which it is possible to prescribe arbitrarily the eigenvalues of C, when three arbitrary positions are prescribed and the remaining are free.
Balanced Double Ockham Algebras
Authors: Blyth T. S. , Fang Jie
Published: February 2014

For a wide class of double Ockham algebras we characterise the subdirectly irreducible members by determining the structure of their lattice of congruences.
Two-parameter Quantum Groups of Exceptional Type E-Series and Convex PBW-type Basis
Authors: Bai Xiaotang , Hu Naihong
Published: February 2014

The presentation of two-parameter quantum groups of type E-series in the sense of Benkart–Witherspoon is given, which has a Drinfel'd quantum double structure. The universal R-matrix and a convex PBW-type basis are described for type E6(as a sample), and the conditions of an isomorphism from these quantum groups into the one-parameter quantum doubles are discussed.
On the Arithmetical Rank of an Intersection of Ideals
Authors: Barile Margherita
Published: February 2014

We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
A Note on Parabolic Subgroups and the Steenrod Algebra Action
Authors: Kechagias Nondas E.
Published: February 2014

The ring of modular invariants of parabolic subgroups has been described by Kuhn and Mitchell using Dickson algebra generators. We provide a new generating set which is closed under the Steenrod algebra action along with the relations between these elements.
Gorenstein Injective Resolutions, Cousin Complexes and Top Local Cohomology Modules
Authors: Khashyarmanesh Kazem
Published: February 2014

Let R be a Gorenstein local ring. We show that for a balanced big Cohen–Macaulay module M over R, the Cousin complex [Formula: see text] provides a Gorenstein injective resolution of M. Also, over a d-dimensional Gorenstein local ring R with maximal ideal 𝔪, we show that [Formula: see text], the dth local cohomology module of M with respect to 𝔪, is Gorenstein injective if (a) M is a balanced big Cohen–Macaulay R-module, or (b) M ∈ G(R), where G(R) is the Auslander's G-class of R.
Nuclei and Lifts of π-Partial Characters
Authors: Lewis Mark L.
Published: February 2014

In this paper, we obtain a common generalization of the Isaacs and Navarro constructions of nuclei for characters of π-separable groups. The construction of Isaacs used the lattice of all subnormal subgroups, and the construction of Navarro used the lattice of all normal subgroups. We show that a generalized nucleus can be constructed using other lattices of subnormal subgroups, and these nuclei have properties similar to the properties of the nuclei constructed by Isaacs and Navarro.
The Probabilistic Zeta Function of Alternating and Symmetric Groups
Authors: Lucchini Andrea , Massa Marilena
Published: February 2014

The probability that a finite group G is generated by s elements is given by a truncated Dirichlet series in s, denoted by PG(s). We give an explicit criterion that allows one to recognize whether the factor group G/ Frat (G) is simple by only looking at the coefficients of PG(s). In order to get such a criterion, we prove that the series derived from PG(s) by removing the even-indexed terms has only a simple zero at s=1.
On 2-Solvable n-Lie Algebras
Authors: Bai Ruipu , Cheng Yu , Liu Xuewen
Published: February 2014

This paper concerns 2-solvable n-Lie algebras L over a field F. We prove that the Cartan subalgebras of L exist when the characteristic of F is not two. We then describe the structure of a class of 2-solvable n-Lie algebras using Frattini subalgebras. At last, we show that the n-Lie algebras in this class are the only 2-solvable n-Lie algebras when the characteristic of the field is zero.
Symplectic Forms on Six-dimensional Real Solvable Lie Algebras I
Authors: Campoamor-Stursberg Rutwig
Published: February 2014

We analyze symplectic forms on six-dimensional real solvable and non-nilpotent Lie algebras. More precisely, we obtain all those algebras endowed with a symplectic form that decompose as the direct sum of two ideals or are indecomposable solvable algebras with a four-dimensional nilradical.
On a Certain Algebra of Higher Modular Forms
Authors: Marschner Axel , Müller Jürgen
Published: February 2014

By a combined use of analytical, algebraic and computational tools, we derive a description of the algebra of modular forms with respect to a certain congruence subgroup of SL 2(ℤ) × SL 2(ℤ) of level 3.
On Subtractive Semisimple Semirings
Authors: Katsov Y. , Nam T. G. , Tuyen N. X.
Published: February 2014

Among other results on subtractive semimodules and semirings, we present various (homological) characterizations of subtractive semisimple semirings. Also, we give complete descriptions of finite subtractive semisimple as well as additively regular (in particular, additively idempotent) subtractive semisimple semirings.
Lie Dimension Subgroups and Central Series Related to Group Algebras
Authors: Spinelli Ernesto
Published: February 2014

Let KG be the group algebra of a group G over a field K of positive characteristic p, and let 𝔇(n)(G) and 𝔇[n](G) denote the n-th upper Lie dimension subgroup and the n-th lower one, respectively. In [1] and [12], the equality 𝔇(n)(G) =𝔇[n](G) is verified when p ≥ 5. Motivated by [16, Problem 55], in the present paper we establish it for particular classes of groups when p ≤ 3. Finally, we introduce and study a new central series of G linked with the Lie nilpotency class of KG.
On the Intersection of Maximal Subalgebras in a Lie Superalgebra
Authors: Chen Liangyun , Meng Daoji
Published: February 2014

The maximal subalgebras and their intersection of a Lie algebra or a Lie superalgebra were studied by Racine, Scheiderer, Elduque, Melikyan, et al. The purpose of the present paper is to continue the investigation in order to obtain deeper structure theorems for Lie superalgebras. We develop the Frattini theory for Lie superalgebras, generalize Barnes's results to Lie superalgebras, and obtain some necessary and sufficient conditions for solvable Lie superalgebras and nilpotent Lie superalgebras. Moreover, some necessary and sufficient conditions for ϕ-free Lie superalgebras and elementary Lie superalgebras are given.
A Characterization of Gorenstein Rings and Grothendieck's Conjecture
Authors: Khashyarmanesh Kazem
Published: February 2014

Given a commutative Noetherian local ring (R, 𝔪), it is shown that R is Gorenstein if and only if there exists a system of parameters x1,…,xd of R which generates an irreducible ideal and [Formula: see text] for all t > 0. Let n be an arbitrary non-negative integer. It is also shown that for an arbitrary ideal 𝔞 of a commutative Noetherian (not necessarily local) ring R and a finitely generated R-module M, [Formula: see text] is finitely generated if and only if there exists an 𝔞-filter regular sequence x1,…,xn∈ 𝔞 such that [Formula: see text] for all t > 0.
Lie Bialgebra Structures on Lie Algebras of Block Type
Authors: Cheng Yongsheng , Song Guang'ai , Xin Bin
Published: February 2014

This paper considers Lie bialgebra structures on Lie algebras of Block type and proves that all such Lie bialgebras are triangular coboundary.
The Zariski Topology on the Prime Spectrum of a Module over Noncommutative Rings
Authors: Tekir Ünsal
Published: February 2014

Let R be an associative ring with identity and M an R-module. Let Spec (M) be the set of all prime submodules of M. We topologize Spec (M) with the Zariski topology and prove some useful results.
$\widetilde{\cal H}$-Supercryptogroups Having Regular Band Congruence
Authors: Yuan Zhiling , Shum K. P.
Published: February 2014

We consider a generalized superabundant semigroup within the class of semiabundant semigroups, called a supercryptogroup since it is an analogy of a cryptogroup in the class of regular semigroups. We prove that a semigroup S is an [Formula: see text]-regular supercryptogroup if and only if S can be expressed as a refined semilattice of completely [Formula: see text]-simple semigroups. Some results on regular cryptogroups are extended to [Formula: see text]-regular supercryptogroups. Some results on superabundant semigroups are also generalized.
Relations of Normal Bundles and Flips of Small Contractions on Projective Manifolds
Authors: Su Jihong , Zhao Yicai
Published: February 2014

Let X be a smooth projective variety over the complex number field. Let f : X → Y be a small contraction, and suppose that each irreducible component Eiof the exceptional locus E of f is a smooth subvariety. Assume that dim E ≤ ½ ( dim X + 1), and the normal bundle [Formula: see text]. Then each Ei≅ Pdim Eior Qdim Ei. Moreover, the flip f+: X+→ Y of f exists.
Lie Nilpotency Indices of Modular Group Algebras
Authors: Bovdi V. , Srivastava J. B.
Published: February 2014

Let K be a field of positive characteristic p and KG the group algebra of a group G. It is known that if KG is Lie nilpotent, then its upper (or lower) Lie nilpotency index is at most |G′| + 1, where |G′| is the order of the commutator subgroup. The class of groups G for which these indices are maximal or almost maximal has already been determined. Here we determine G for which upper (or lower) Lie nilpotency index is the next highest possible.
The Preimage of a Coordinate
Authors: Gong Sheng-Jun , Yu Jie-Tai
Published: February 2014

Let K be a field of characteristic zero. Based on the degree estimate of Makar-Limanov and Yu, we prove that the preimage of a coordinate under an injective endomorphism of K〈x, y〉 is also a coordinate. As by-products, we give new proofs of the following results: (1) the preimage of a coordinate under an injective endomorphism of K[x,y] is also a coordinate; (2) any automorphism of K[x,y] or K〈x, y〉 is tame.
Linkage and Strongly Generalized Cohen–Macaulay Ideals
Authors: Hassanzadeh S. H. , Shirmohammadi N. , Zakeri H.
Published: February 2014

The notion of SGCM ideals is introduced as an extension of the known notion of SCM ideals. Some properties of SGCM ideals, which are closely related to SCM ideals in a Gorenstein local ring, are given. It turns out that the SGCM property is retained through the even linkage class in a Gorenstein local ring. Also, we establish the equality of the finiteness dimension of the residue class rings of two evenly linked ideals. Finally, some slight relations between SGCM ideals and CM d-sequences are obtained.
A Kind of Graph Structure on Non-reduced Rings
Authors: Li Aihua , Li Qisheng
Published: February 2014

In this paper, a kind of graph structure ΓN(R) of a ring R is introduced, and the interplay between the ring-theoretic properties of R and the graph-theoretic properties of ΓN(R) is investigated. It is shown that if R is Artinian or commutative, then ΓN(R) is connected, the diameter of ΓN(R) is at most 3; and if ΓN(R) contains a cycle, then the girth of ΓN(R) is not more than 4; moreover, if R is non-reduced, then the girth of ΓN(R) is 3. For a finite commutative ring R, it is proved that the edge chromatic number of ΓN(R) is equal to the maximum degree of ΓN(R) unless R is a nilpotent ring with even order. It is also shown that, with two exceptions, if R is a finite reduced commutative ring and S is a commutative ring which is not an integral domain and ΓN(R) ≃ ΓN(S), then R ≃ S. If R and S are finite non-reduced commutative rings and ΓN(R) ≃ ΓN(S), then |R|=|S| and |N(R)|=|N(S)|.
Lie Bialgebra Structures on the Centerless W-Algebra W(2,2)
Authors: Li Junbo , Su Yucai , Xin Bin
Published: February 2014

Verma modules over the W-algebra W(2,2) were considered by Zhang and Dong, while the Harish-Chandra modules and irreducible weight modules over this algebra were classified by Liu and Zhu etc. In the present paper, we investigate the Lie bialgebra structures on the centerless W-algebra, which are shown to be triangular coboundary.
Embedding Regular Semigroups into Idempotent Generated Ones
Authors: Petrich Mario
Published: February 2014

Any semigroup S can be embedded into a semigroup, denoted by ΨS, having some remarkable properties. For general semigroups there is a close relationship between local submonoids of S and of ΨS. For a number of usual semigroup properties [Formula: see text], we prove that S and ΨS simultaneously satisfy [Formula: see text] or not. For a regular semigroup S, the relationship of S and ΨS is even closer, especially regarding the natural partial order and Green's relations; in addition, every element of ΨS is a product of at most four idempotents. For completely regular semigroups S, the relationship of S and ΨS is still closer. On the lattice [Formula: see text] of varieties of completely regular semigroups [Formula: see text] regarded as algebras with multiplication and inversion, by means of ΨS, we define an operator, denoted by Ψ. We compare Ψ with some of the standard operators on [Formula: see text] and evaluate it on a small sublattice of [Formula: see text].
Extended Semicommutative Rings
Authors: Başer Muhittin , Kwak Tai Keun
Published: February 2014

An endomorphism α of a ring R is called semicommutative if ab = 0 implies aR α(b) = 0 for a, b ∈ R, and R is called an α-semicommutative ring if there exists a semicommutative endomorphism α of R. The notion of an α-semicommutative ring is an extension of semicommutative rings as well as a generalization of α-rigid rings. We investigate its related properties and the relationship between α-semicommutative rings and extended Armendariz rings.
Local Generalized Derivations in Prime Rings with Idempotents
Authors: Wang Yu
Published: February 2014

Let R be a prime ring with a nontrivial idempotent. In this paper, we prove that if g is an additive map of R into itself such that xg(y)z = 0 for all x, y, z ∈ R with xy = yz = 0, then g is a generalized derivation. As an application of this result, we show that every local generalized derivation in a prime ring with a nontrivial idempotent is a generalized derivation.
Row-finite Matrices and Power Series Near-rings
Authors: Lee K. S. Enoch
Published: February 2014

We define and investigate (structural) row-finite matrices, lower triangular matrices, and power series in near-rings by using inverse limits of some special classes of matrices. Our approach is different from that described in [8]. We show that polynomials can be embedded in power series and power series can be embedded in lower triangular matrices as in rings. We extend the concept of order of a polynomial (or a power series) from rings to near-rings. A natural topology is defined on lower triangular matrices by generalizing the concept of order of power series. We also obtain some results concerning prime and completely prime ideals in lower triangular matrix near-rings.
A Note on the Classical Dickson Invariants
Authors: Jow Shin-Yao
Published: February 2014

Let 𝔽q be the finite field with q elements, where q is a power of some prime p. In the classical paper [2], Dickson defined the polynomial [Formula: see text], where e1,…, en are non-negative integers. He observed that any [e1,…, en] is divisible by [0,1,…,n-1], and the quotient is GL n(𝔽q)-invariant. He then went on to show that one can pick n of these invariants to generate the entire invariant subring of GL n(𝔽q). In this paper, we answer the following two natural questions: How to express any given [e1,…, en]/[0,1,…,n-1] in terms of the fundamental generators? In general, when does [e1,…, en] divide [f1,…, fn]? The answers are Theorems 1.2 and 1.3, respectively.
Leibniz Algebras Graded by Finite Root Systems
Authors: Liu Dong , Hu Naihong
Published: February 2014

Several authors investigate Lie algebras and Lie superalgebras graded by finite root systems. In this paper, we study Leibniz algebras graded by finite root systems and obtain some results in simply-laced cases.
Centralizer of Engel Elements in a Group
Authors: Endimioni Gérard , Sica Carmela
Published: February 2014

In this paper we show that some finiteness properties on a centralizer of a particular subgroup can be inherited by the whole group. Among other things, we prove the following characterization of polycyclic groups: a soluble group G is polycyclic if and only if it contains a finitely generated subgroup H, formed by bounded left Engel elements, whose centralizer CG(H) is polycyclic. In the context of Černikov groups we obtain a more general result: a radical group is a Černikov group if and only if it contains a finitely generated subgroup, formed by left Engel elements, whose centralizer is a Černikov group. The aforementioned results generalize a theorem by Onishchuk and Zaĭtsev about the centralizer of a finitely generated subgroup in a nilpotent group.
One-point Extensions and Recollements of Derived Categories
Authors: Lin Yanan , Lin Zengqiang
Published: February 2014

Let A be a finite dimensional algebra over an arbitrary field k. Assume that a bounded above derived category D-( Mod A) admits a recollement relative to bounded above derived categories of two finite dimensional k-algebras B and C: [Formula: see text] In this paper, we prove that if there exist M ∈ mod A and N ∈ mod B such that i⋆(N)=M, then the bounded above derived category D-( Mod A[M]) admits a recollement relative to bounded above derived categories of two finite dimensional k-algebras B[N] and C: [Formula: see text] where A[M] and B[N] are the one-point extensions of A by M and of B by N, respectively. As a consequence, we obtain the main result of Barot and Lenzing [1].
Brauer Characters of Prime Power Degrees and Conjugacy Classes of Prime Power Lengths
Authors: Tiep Pham Huu , Willems Wolfgang
Published: February 2014

We study the structure of any finite group in which the degree of every irreducible p-Brauer character, respectively the length of every p-regular conjugacy class, is a power of a fixed prime.
On Lattices of Formations of Finite Groups
Authors: Shemetkov L. A. , Skiba A. N. , Vorob'ev N. N.
Published: February 2014

Let ω be a set of primes with |ω| > 1, and m > n ≥ 0 be integers. It is proved that the lattice of all τ-closed m-multiply ω-saturated formations is not a sublattice of the lattice of all τ-closed n-multiply ω-saturated formations.
Ockham Algebras with Balanced Demi-pseudocomplementation
Authors: Fang Jie
Published: February 2014

Let bdpO be the variety consisting of those algebras (L; ∧, ∨, f, *,0,1) of type 〈2,2,1,1,0,0〉, where (L; ∧, ∨, f,0,1) is an Ockham algebra, (L; ∧, ∨, *,0,1) is a demi-pseudocompleted lattice, and the unary operations f and * satisfy the conditions [f(x)]*=f2(x) and f(x*)=x**. Here we give a description of the structure of the subdirectly irreducible algebras in bdpO.
Lie Algebras with Abelian Centralizers
Authors: Klep Igor , Moravec Primož
Published: February 2014

We classify all finite-dimensional Lie algebras over an algebraically closed field of characteristic 0, whose nonzero elements have abelian centralizers. These algebras are either simple or solvable, where the only simple such Lie algebra is [Formula: see text]. In the solvable case, they are either abelian or a one-dimensional split extension of an abelian Lie algebra.
On Braided Lie Structures of Algebras in the Categories of Weak Hopf Bimodules
Authors: Wang Shuan-hong , Zhu Hai-xing
Published: February 2014

Let H be a weak Hopf algebra. In this paper, it is proved that the monoidal category [Formula: see text] of weak Hopf bimodules studied in Wang [19] is equivalent to the monoidal category [Formula: see text] of weak Yetter–Drinfel'd modules introduced in Böhm [2]. When H has a bijective antipode, a braiding in the category [Formula: see text] is constructed by the braiding on [Formula: see text], generalizing the main result in Schauenburg [14]. Finally, the braided Lie structures of an algebra A in the category [Formula: see text] are investigated, by showing that if A is a sum of two braided commutative subalgebras, then the braided commutator ideal of A is nilpotent.
Array Codes in the Generalized Lee-RT Pseudo-Metric (GLRTP-Metric)
Authors: Jain Sapna
Published: February 2014

In this paper, we introduce a pseudo-metric on the space of all m × s matrices with entries from the finite ring Zq, generalizing the classical Lee metric and the array RT metric, and name this pseudo-metric as the generalized Lee-RT pseudo-metric (or the GLRTP-metric). We also obtain some bounds on the parameters of array codes equipped with the GLRTP-metric.
Formally-radical Functions in Elements of a Nilpotent Lie Algebra and Noncommutative Localizations
Authors: Dosi Anar
Published: February 2014

In the present paper, we introduce the sheaf 𝔗𝔤of germs of non-commutative holomorphic functions in elements of a finite-dimensional nilpotent Lie algebra 𝔤, which is a sheaf of non-commutative Fréchet algebras over the character space of 𝔤. We prove that 𝔗𝔤(D) is a localization over the universal enveloping algebra [Formula: see text] whenever D is a polydisk, which in turn allows to describe the Taylor spectrum of a supernilpotent Lie algebra of operators in terms of the transversality.
On Flexible Algebras Satisfying x(yz) = y(zx)
Authors: Behn Antonio , Correa Ivan , Hentzel Irvin Roy
Published: February 2014

In this paper we study flexible algebras (possibly infinite-dimensional) satisfying the polynomial identity x(yz) = y(zx). We prove that in these algebras, products of five elements are associative and commutative. As a consequence of this, we get that when such an algebra is a nil-algebra of bounded nil-index, it is nilpotent. Furthermore, we obtain optimal bounds for the index of nilpotency. Another consequence that we get is that these algebras are associative when they are semiprime.
Symmetric Words in Dihedral Groups
Authors: Płonka Ernest
Published: February 2014

Let G be a group and let w = w(x1, x2,…, xn) be a word in the absolutely free group Fnon free variables x1, x2,…, xn. The set S(n)(G) of all words w such that the equality w(gσ1, gσ2,…, gσn) = w(g1, g2,…, gn) holds for all g1, g2,…, gn∈G and all permutations σ ∈ Snis a subgroup of Fn, called the subgroup of n-symmetric words for G. In this paper, the groups S(2)(Dp) and S(3)(Dp) for dihedral groups Dpare determined, where p > 3 is a prime. In particular, it turns out that the groups S(3)(Dp) are not abelian.
Clifford Algebra Realization of Certain Infinite-dimensional Lie Algebras
Authors: Li Li , Wang Chunyan , Du Xiufeng
Published: February 2014

We give a Clifford algebra realization of a certain family of infinite-dimensional Lie algebras, inspired by a result of Berman, Gao and Tan. Furthermore, we relate this realization with vertex superalgebras and quasi modules.
On Duo Group Rings
Authors: Gao Weidong , Li Yuanlin
Published: February 2014

It is shown that if the group ring RQ8 of the quaternion group Q8 of order 8 over an integral domain R is duo, then R is a field for the following cases: (1) char R ≠ 0, and (2) char R = 0 and S ⊆ R ⊆ KS, where S is a ring of algebraic integers and KS is its quotient field. Hence, we confirm that the field ℚ of rational numbers is the smallest integral domain R of characteristic zero such that RQ8 is duo. A non-field integral domain R of characteristic zero for which RQ8 is duo is also identified. Moreover, we give a description of when the group ring RG of a torsion group G is duo.
Hochschild Cohomology Ring of the Integral Group Ring of the Semidihedral 2-Group
Authors: Hayami Takao
Published: February 2014

We determine the ring structure of the Hochschild cohomology HH*(ℤ G) of the integral group ring of the semidihedral 2-group G = SD2rof order 2r.
Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups
Authors: Golasiński Marek , Gonçalves Daciberg Lima
Published: February 2014

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut (G).
Linear Groups with Bounded Action
Authors: Dixon Martyn R. , Kurdachenko Leonid A. , Otal Javier
Published: February 2014

If R is a ring, G a group and A a right RG-module, then G has boundedly finite orbits on A if there is a positive integer b such that for all a ∈ A, the set {ag | g ∈ G} has order at most b. We study groups G with this property, proving that G/CG(A) is abelian-by-finite and that it is quite often the case that G/CG(A) is finite.
Finite Exchange Property for Quasi-projective Modules
Authors: Chen Huanyin
Published: February 2014

In this paper, we obtain several necessary and sufficient conditions under which a quasi-projective module has the finite exchange property. Applications to finitely generated modules are also studied. These extend some corresponding results on exchange rings.
Simple Deformed Witt Algebras
Authors: Song Guang'ai , Xia Chunguang
Published: February 2014

For any unique factorization domain [Formula: see text] and an algebra endomorphism σ of [Formula: see text], there exists a non-associative algebra [Formula: see text] with multiplication satisfying skew-symmetry and generalized (twisted) Jacobi identities, called a σ-deformed Witt algebra. In this paper, we obtain necessary and sufficient conditions for the algebra [Formula: see text] to be simple.
On Zero-divisor Graphs Whose Cores Contain no Rectangles
Authors: Liu Qiong , Wu Tongsuo
Published: February 2014

This paper answers a question of Lu and Wu: How can one characterize the zero-divisor graphs which contain no rectangles? We prove that a graph which contains no rectangles is the zero-divisor graph of a semigroup with 0 if and only if it is one of the following graphs: an isolated vertex, a star graph, a two-star graph, a triangle with n horns (n = 0, 1, 2, 3), a fan graph, a fan graph with a horn adjacent to its center. In addition, we completely determine the correspondence between commutative rings and finite zero-divisor graphs which contain no rectangles.
Lie Bialgebra Structures on the Extended Schrödinger-Virasoro Lie Algebra
Authors: Yuan Lamei , Wu Yongping , Xu Ying
Published: February 2014

In this paper, Lie bialgebra structures on the extended Schrödinger-Virasoro Lie algebra [Formula: see text] are classified. It is obtained that all the Lie bialgebra structures on [Formula: see text] are triangular coboundary. As a by-product, it is derived that the first cohomology group [Formula: see text] is trivial.
A Note on Bessel Functions for Supercuspidal Representations of GL(2) over a p-Adic Field
Authors: Baruch Ehud Moshe , Snitz Kobi
Published: February 2014

We compute the Bessel functions which give the action of the Weyl group element in the Kirillov model of supercuspidal representations of GL 2(K), where Kis a p-adic field. Together with the known action of the Borel subgroup, this gives the full action of GL 2(K) for such representations. We consider supercuspidal representations constructed by Jacquet and Langlands using the Weil representation. When the residual characteristic is odd, these are all the supercuspidal representations, hence we get a full description of all supercuspidal representations in this case.
Canonical Forms and Infimum of Positive Braids
Authors: Ali U. , Iqbal Z. , Nazir S.
Published: February 2014

In this paper, we prove that a subset of the non-commutative Gröbner basis for the braid group given by Bokut is a basis for the braid monoid in band generators. We give an inductive way of computing the infimum of a positive braid and hence a criteria to decide whether a positive word is prime to the fundamental braid or not. We also compute the Hilbert series of the braid monoid with three generators.
Hilbert Series of Positive Braids
Authors: Iqbal Zaffar
Published: February 2014

Deligne proved that the Hilbert series of all Artin monoids are rational functions. We give an algorithm to compute the Hilbert series of the braid monoids [Formula: see text]. We also show that the Hilbert series of the positive words in [Formula: see text] with a given prefix are rational functions.
On Uσ-Abundant Semigroups
Authors: Ren Xueming , Yin Qingyan , Shum K. P.
Published: February 2014

A U-abundant semigroup whose subset U satisfies a permutation identity is said to be Uσ-abundant. In this paper, we consider the minimum Ehresmann congruence δ on a Uσ-abundant semigroup and explore the relationship between the category of Uσ-abundant semigroups (S,U) and the category of Ehresmann semigroups (S,U)/δ. We also establish a structure theorem of Uσ-abundant semigroups by using the concept of quasi-spined product of semigroups. This generalizes a result of Yamada for regular semigroups in 1967 and a result of Guo for abundant semigroups in 1997.
On the Structure of Augmentation Quotient Groups for the Generalized Quaternion Group
Authors: Zhou Qingxia , You Hong
Published: February 2014

For the generalized quaternion group G, this article deals with the problem of presenting the nth power Δn(G) of the augmentation ideal Δ (G) of the integral group ring ZG. The structure of Qn(G)=Δn(G)/Δn+1(G) is obtained.
On Classes of Local Unitary Transformations
Authors: Jing Naihuan
Published: February 2014

We give a one-to-one correspondence between classes of density matrices under local unitary invariance and the double cosets of unitary groups. We show that the interrelationship among classes of local unitary equivalent multi-partite mixed states is independent from the actual values of the eigenvalues and only depends on the multiplicities of the eigenvalues. The interpretation in terms of homogeneous spaces of unitary groups is also discussed.
On the Endomorphism Monoid of K(n,3)
Authors: Hou Hailong , Luo Yanfeng , Gu Rui
Published: February 2014

In this paper, the endomorphism monoid of circulant complete graph K(n,3) is explored explicitly. It is shown that Aut K(n,3)) =Dn, the dihedral group of degree n. It is also shown that K(n,3) is unretractive when 3 does not divide n, End (K(3m,3)) = qEnd (K(3m,3)), sEnd (K(3m,3)) = Aut (K(3m,3)) and K(3m,3) is endomorphism-regular. The structure of End (K(3m,3)) is characterized and some enumerative problems concerning End (K(n,3)) are solved.
S-Lattice Congruences of S-Lattices
Authors: Luo Congwen
Published: February 2014

In this paper, the S-lattices are introduced as a representation of lattice-ordered monoids. The smallest S-lattice congruence induced by a relation on an S-lattice is characterized and the correspondence between the S-lattice congruences and S-ideals in an S-distributive lattice is discussed. These generalize some recent results of lattices and lattice-ordered semigroups.
Derived Hall Algebras and Lattice Algebras
Authors: Sheng Jie , Xu Fan
Published: February 2014

The aim of this paper is to compare Kapranov's lattice algebra with Toën's derived Hall algebra. We prove that the derived Hall algebra can be identified with the lattice algebra by the “twist and extend” procedure with a suitable subalgebra closely related to the Heisenberg double.
The Lattice of Congruences on a Subdirectly Irreducible Weak Stone-Ockham Algebra
Authors: Fang Jie
Published: February 2014

Weak Stone-Ockham algebras are those algebras (L; ∧, ∨, f,⋆,0,1) of type 〈2,2,1,1,0,0〉, where (L; ∧, ∨, f,0,1) is an Ockham algebra, (L; ∧, ∨,⋆,0,1) is a weak Stone algebra, and the unary operations f and⋆commute. In this paper, we give a complete description of the structure of the lattice of congruences on the subdirectly irreducible algebras.
Derivations and Automorphism Group of Completed Witt Lie Algebra
Authors: Wu Yongping , Xu Ying , Yuan Lamei
Published: February 2014

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.
On Quasipolar Rings
Authors: Ying Zhiling , Chen Jianlong
Published: February 2014

The notion of quasipolar elements of rings was introduced by Koliha and Patricio in 2002. In this paper, we introduce the notion of quasipolar rings and relate it to other familiar notions in ring theory. It is proved that both strongly π-regular rings and uniquely clean rings are quasipolar, and quasipolar rings are strongly clean, but no two of these classes of rings are equivalent. For commutative rings, quasipolar rings coincide with semiregular rings. It is also proved that every n × n upper triangular matrix ring over any commutative uniquely clean ring or commutative local ring is quasipolar.
Noetherianness and Local Cohomology Modules
Authors: Khashyarmanesh Kazem
Published: February 2014

Let R be a commutative Noetherian ring, 𝔞 an ideal of R, and M an R-module. We show that, whenever [Formula: see text], M is Noetherian if and only if there exists a submodule N of M such that the R-modules M/𝔞 N and [Formula: see text] are Noetherian. By using this result, we establish Noetherian properties for local cohomology modules [Formula: see text] in several cases. For instance, we obtain a new version of the Lichtenbaum-Hartshorne Vanishing Theorem.
f-Ideals of Degree 2
Authors: Abbasi G. Q. , Ahmad S. , Anwar I. , Baig W. A.
Published: February 2014

In this paper, we introduce the concept of f-ideals and discuss its algebraic properties. In particular, we give a characterization of all the f-ideals of degree 2.
Sn-Normal Semigroups of Partial Transformations
Authors: Droms Sean V. , Konieczny Janusz , Palomba Roberto
Published: February 2014

For an integer n ≥ 1, let [Formula: see text] and Snbe, respectively, the semigroup of partial transformations and the symmetric group on the set X = {1,…,n}. Then Snis the group of units of [Formula: see text]. A subsemigroup S of [Formula: see text] is Sn-normal if for all a ∈ S and g ∈ Sn, g-1ag ∈ S. In 1976, Symons described the Sn-normal semigroups of full transformations of X. In 1995, Lipscomb and the second author determined the Sn-normal semigroups of partial injective transformations of X. In this paper, we complete the classification by describing all Sn-normal subsemigroups of [Formula: see text]. As a consequence of the classification theorem, we obtain a characterization of the automorphisms of any Sn-normal subsemigroup of [Formula: see text].
The Non-abelian Tensor Square and Schur Multiplier of Groups of Orders p2q and p2qr
Authors: Jafari S. H. , Niroomand P. , Erfanian A.
Published: February 2014

The aim of this paper is to determine the non-abelian tensor square and Schur multiplier of groups of square-free orders and of groups of orders p2q, pq2and p2qr, where p, q and r are primes and p < q < r.
On Maximal Subrings of Commutative Rings
Authors: Azarang A. , Karamzadeh O. A. S.
Published: February 2014

A proper subring S of a ring R is said to be maximal if there is no subring of R properly between S and R. If R is a noetherian domain with |R| > 2ℵ0, then | Max (R)| ≤ | RgMax (R)|, where RgMax (R) is the set of maximal subrings of R. A useful criterion for the existence of maximal subrings in any ring R is also given. It is observed that if S is a maximal subring of a ring R, then S is artinian if and only if R is artinian and integral over S. Surprisingly, it is shown that any infinite direct product of rings has always maximal subrings. Finally, maximal subrings of zero-dimensional rings are also investigated.
Most Commutative Rings Have Maximal Subrings
Authors: Azarang A. , Karamzadeh O. A. S.
Published: February 2014

It is shown that if R is a ring with unit element which is not algebraic over the prime subring of R, then R has a maximal subring. It is shown that whenever R ⊆ T are rings such that there exists a maximal subring V of T, which is integrally closed in T and U(R) ⊈ V, then R has a maximal subring. In particular, it is proved that if R is algebraic over ℤ and there exists a natural number n > 1 with n ∈ U(R), then R has a maximal subring. It is shown that if R is an infinite direct product of certain fields, then the maximal ideals M for which RM(R/M) has maximal subrings are characterized. It is observed that if R is a ring, then either R has a maximal subring or it must be a Hilbert ring. In particular, every reduced ring R with |R|>22ℵ0or J(R) ≠ 0 has a maximal subring. Finally, the semi-local rings having maximal subrings are fully characterized.
On Relative n-Auslander-Reiten Isomorphisms
Authors: Wang Yao , Zhang Xiaojin
Published: February 2014

We generalize the Auslander-Reiten isomorphisms to the relative n-Auslander-Reiten isomorphisms.
Lifting of Outer Actions of Groups II
Authors: Zhou Fang , Liu Heguo
Published: February 2014

In this paper we continue to study the lifting of outer actions of groups and introduce the concept of equivalence of two lifting homomorphisms, maximal lifting homomorphisms and maximal split extensions. Some criteria are obtained.
The Representations of Quantum Double of Dihedral Groups
Authors: Dong Jingcheng , Chen Huixiang
Published: February 2014

Let k be an algebraically closed field of odd characteristic p, and let Dn be the dihedral group of order 2n such that p|2n. Let D(kDn) denote the quantum double of the group algebra kDn. In this paper, we describe the structures of all finite-dimensional indecomposable left D(kDn)-modules, equivalently, of all finite-dimensional indecomposable Yetter-Drinfeld kDn-modules, and classify them.
Extending Endo-monomial Modules
Authors: Lu Ziqun , Zhang Jiping
Published: February 2014

Let G be a finite group with a normal Sylow p-subgroup P. Let [Formula: see text] be a complete discrete valuation ring with residue field F of characteristic p. Let M be an indecomposable endo-monomial [Formula: see text]-module. In this paper we prove that M extends to an [Formula: see text]-module if and only if M is G-stable. A similar and well-known version for endo-permutation modules is due to Dade.
Derivations and Automorphisms of a Lie Algebra of Block Type
Authors: Xia Chunguang , Wang Wei
Published: February 2014

Let [Formula: see text] be a Lie algebra of Block type with basis {Lα,i| α ∈ ℤ, i ∈ ℤ+} and relations [Lα,i,Lβ,j]= ((α-1)(j+1)-(β-1)(i+1))Lα+β, i+j. In the present paper, the derivation algebra and automorphism group of [Formula: see text] are explicitly described. In particular, it is shown that the outer derivation space is 1-dimensional and the inner automorphism group of [Formula: see text] is trivial.
Quasi-finite Irreducible Graded Modules for the Virasoro-like Algebra
Authors: Lin Weiqiang , Su Yucai
Published: February 2014

In this paper, we consider the classification of irreducible Z- and Z2-graded modules with finite-dimensional homogeneous subspaces over the Virasoro-like algebra. We prove that such a module is a uniformly bounded module or a generalized highest weight module. Then we determine all generalized highest weight quasi-finite irreducible modules. As a consequence, we determine all the modules with nonzero center. Finally, we prove that there does not exist any non-trivial Z-graded module of intermediate series.
Finite p-Groups in Which Any Two Noncommutative Elements Generate an Inner Abelian Group of Order p4
Authors: An Lijian , Peng Juan
Published: February 2014

In this paper, finite p-groups in which any two noncommutative elements generate an inner abelian group of order p4 are classified.
Quantum Deformations of the Heisenberg-Virasoro Algebra
Authors: Cheng Yongsheng , Su Yucai
Published: February 2014

In this paper, the authors develop an approach to construct a q-deformed Heisenberg-Virasoro algebra which is a Hom-Lie algebra, and investigate its central extensions and second cohomology group. Finally, quantum deformations of the Heisenberg-Virasoro algebra which provide a non-trivial Hopf structure are presented.
Smith Normal Form of Augmented Degree Matrix and Rational Points on Toric Hypersurface
Authors: Chen Jianming , Cao Wei
Published: February 2014

We use the Smith normal form of the augmented degree matrix to estimate the number of rational points on a toric hypersurface over a finite field. This is the continuation of a previous work by Cao in 2009.
On the Intersection of the Normalizers of the Nilpotent Residuals of All Subgroups of a Finite Group
Authors: Gong Lü , Guo Xiuyun
Published: February 2014

In this paper, a characteristic subgroup [Formula: see text] of a finite group G is defined, which is the intersection of the normalizers of the nilpotent residuals of all subgroups of G, and the properties of [Formula: see text] and the relationship between [Formula: see text] and the group G are investigated.
On Efficient Presentations for Infinite Sequences of 2-Groups with Fixed Coclass
Authors: Abdolzadeh Hossein , Eick Bettina
Published: February 2014

Eick and Leedham-Green introduced infinite sequences of finite p-groups of fixed coclass. They showed that the groups in such an infinite sequence can be defined by a single parametrised presentation. Our aim is to construct short or even efficient parametrised presentations for such infinite sequences of finite 2-groups.
Ding Projective and Ding Injective Modules
Authors: Yang Gang , Liu Zhongkui , Liang Li
Published: February 2014

An R-module M is called Ding projective if there exists an exact sequence ⋯ → P1→ P0→ P0→ P1→ ⋯ of projective R-modules with M= Ker (P0→ P1) such that Hom (-,F) leaves the sequence exact whenever F is a flat R-module. In this paper, we develop some basic properties of such modules. Also, properties of Ding injective modules are discussed.
Identities with Product of Generalized Derivations of Prime Rings
Authors: Carini Luisa , De Filippis Vincenzo , Scudo Giovanni
Published: February 2014

Let R be a non-commutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, f(x1,…,xn) a multilinear polynomial over C which is not an identity for R, F and G two non-zero generalized derivations of R. If F(u)G(u)=0 for all u ∈ f(R)= {f(r1,…,rn): ri∈ R}, then one of the following holds: (i) There exist a, c ∈ U such that ac=0 and F(x)=xa, G(x)=cx for all x ∈ R; (ii) f(x1,…,xn)2is central valued on R and there exist a, c ∈ U such that ac=0 and F(x)=ax, G(x)=xc for all x ∈ R; (iii) f(x1,…,xn) is central valued on R and there exist a,b,c,q ∈ U such that (a+b)(c+q)=0 and F(x)=ax+xb, G(x)=cx+xq for all x ∈ R.
ESTABLISHING RELATIONSHIPS BETWEEN INNOVATION CHARACTERISTICS AND IT INNOVATION ADOPTION IN ORGANISATIONS: A META-ANALYSIS APPROACH
Authors: HAMEED MUMTAZ ABDUL , COUNSELL STEVE
Published: February 2014

This paper presents the findings of a meta-analysis of innovation characteristics that influence the adoption of information technology (IT) in organisations. Past studies that examine the determinants of IT innovation adoption have produced inconsistent and contradictory results and deducing a definitive set of attributes for innovation adoption has become impractical. The study has aggregated findings of past research on IT adoption using meta-analysis to identify key factors in terms of innovation or technology that influences adoption of IT in organisation. Six innovation characteristics most commonly examined by researchers have been analysed. The results of this meta-analysis confirm that relative advantage, compatibility, cost, observability and trialability are strong determinants of IT innovation adoption. However, the study found no association between complexity and IT innovation adoption. The effect of stage of innovation, type of innovation, type of organisation and size of organisation as four moderating conditions has also been examined.
CONTINUUM SHELL MODEL FOR BUCKLING OF ARMCHAIR CARBON NANOTUBES UNDER COMPRESSION OR TORSION
Authors: ROY CHOWDHURY A. N. , WANG C. M. , KOH S. J. A.
Published: February 2014

Molecular dynamics (MD) simulations are performed using adaptive intermolecular reactive bond order potential to analyze single-walled and double-walled carbon nanotubes. These carbon nanotubes were analyzed for buckling under compression and under torsion. The MD simulations create a comprehensive database for the critical buckling loads/strains and critical buckling torques/twist angles for armchair SWCNTs and DWCNTs of varying diameters and lengths. Using MD results as a computational benchmark, an equivalent thick shell model of CNT is proposed, which is amenable for analysis using a commercially available software ABAQUS. Based on our MD results, an empirical equation that describes the size-dependent Young's modulus for a single-walled carbon nanotube is established. Buckling analysis of CNT under compression and under torsion are performed with the equivalent shell model using size-dependent Young's modulus, Poisson's ratio = 0.19 and shell thickness h = 0.066 nm. We show that the equivalent shell model gives good estimate of critical buckling load/strain and critical buckling torque with respect to the MD results. Variation of critical twist angle with length of CNT, predicted by the shell model is in good qualitative agreement with MD simulation. However, the equivalent shell model underestimates the critical twist angle by 30% because the continuum shell model overestimates torsional stiffness of CNT compared to an atomistic model of CNT. The equivalent shell model is less computational intensive to implement as compared with MD. Its accuracy for predicting the buckling states for long carbon nanotubes allows it to be used for moderately long CNTs under compression/torsion, in-lieu of MD simulations.