bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semigroup ideals in rings
Authors: Hill David A. 
Published: April 2009

AbstractA ringRis called anl-ring (r-ring) in caseRcontains an indentity and every left (right) semigroup ideal is a left (right) ring ideal. A number of structure theorems are obtained forl-rings whenRis left noetherian and left artinian. It is shown that left noetherianl-rings are local left principal ideal rings. WhenRis a finite dimensional algebra over a field, the property of being anl-ring is equivalent to being anr-ring. However, examples are given to show that these two concepts are in general not equivalent even in the artinian case.
Formulae for well formed formulae and their enumeration
Authors: Tamari Dov 
Published: April 2009

1. General Idea. In this paper formal operators and bracketings devices are essentially the same; so are well formed formulae and correct bracketings.A well known theorem of symbolic logic (Post languages, etc.) and universal algebra characterizes well formed formulae among (linear) strings of symbols for variables and operators in terms of a system of numerical inequalities, one of them an equality.
Varieties and simple groups
Authors: Jones Gareth A. 
Published: April 2009

In her book on varieties of groups, Hanna Neumann posed the following problem [13, p. 166]: “Can a variety other than D contain an infinite number of non-isomorphic non-abelian finite simple groups?”The answer to this question does not seem to be known at present. However, in [7], Heineken and Neumann described an algorithm for determining whether or not there are any non-abelian finite simple groups satisfying a given law. They also outlined a way in which their algorithm could be used to show that “only finitely many of the known non-abelian finite simple groups can satisfy a given non-trivial law”; in this paper, we shall follow their suggestions, and prove theTHEOREM. Let g be a set of mutually non-isomorphic non-abelian finite simple groups, each of which is either an alternating group or a group of Lie type, and let g generate a proper subvariety of D. Then y is finite.
Π′-closure of finite Π-solvable groups
Authors: Arad Zvi 
Published: April 2009

AbstractThe purpose of this paper is to present a proof of the following theorem: Suppose Π is a set of dd primes, G is a finite Π-solvable group, and A is a nilpotent Π-subgroup of maximal order of G. Then G has a normal Π-complement, if and only if NG(ZJ(A)) has a normal Π-complement. (J(A) is the Thompson subgroup of A.)
Inverse semigroups determined by their lattices of inverse subsemigroups
Authors: Jones P. R. 
Published: April 2009

AbstractIn a previous paper ([14]) the author showed that a free inverse semigroup is determined by its lattice of inverse subsemigroups, in the sense that for any inverse semigroup T, implies . (In fact, the lattice isomorphism is induced by an isomorphism of upon T.) In this paper the results leading up to that theorem are generalized (from completely semisimple to arbitrary inverse semigroups) and applied to various classes, including simple, fundamental and E-unitary inverse semigroups. In particular it is shown that the free product of two groups in the category of inverse semigroups is determined by its lattice of inverse subsemigroups.
Set mappings defined on pairs
Authors: Williams N. H. 
Published: April 2009

AbstractA set mapping on pairs over the set S is a function f such that for each unordered pair a of elements of S,f(a) is a subset of S disjoint from a. A subset H of S is said to be free for f if x∉ f({y, z}) for all x, y, z from H. In this paper, we investigate conditions imposed on the range of f which ensure that there is a large set free for f. For example, we show that if f is defined on a set of size K+ + with always |f(a)| <k then f has a free set of size K+ if the range of f satisfies the k-chain condition, or if any two sets in the range of f have an intersection of size less than θ for some θ with θ < K.
Entire solutions of the differential equation Δ;u = f(u)
Authors: Walter Wolfgang 
Published: April 2009

AbstractThe existence of spherically symmetric solutions of the equation ▵u = f(u) is proved for a large class of functions f(z). Among others, functions satisfying an inequality zf(z) < 0 for |z| > A, and in particular the function f(z) = -sinh z, belong to this class.
On Fitting classes that are Schunck classes
Authors: Cossey John 
Published: April 2009

AbstractAn example is given to show that a class of finite soluble groups that is both a Fitting class and a Schunck class need not be a formation. The novel feature of this class is that it is defined by imposing conditions on complemented chief factors of groups in it: this technique usually does not give rise to Fitting classes that are not formations.
Dense, uniform and densely subuniform chains
Authors: Ash C. J. 
Published: April 2009

AbstractA chain, or linearly ordered set, is densely subuniform if it is dense and for every order type the elements whose corresponding initial sections have this order type, if any, are dense in the chain. It is uniform if all intial sections are isomorphic. This paper gives constructions for densely subuniform chains which are not uniform. The question arises from the study of congruence-free inverse semigroups, but may also have independent interest.
The spectrum of an R-homomorphism
Authors: Wickstead A. W. 
Published: April 2009

AbstractLet E be a real Banach space ordered by a closed, normal and generating cone. Suppose also that the order induced on E has the Riesz decomposition property. It is shown that if T:E → E is a positive linear operator with the property that y, z, a ∈ E with a ≧ Ty, Tz implies there is x ∈ E with x ≧ y, z and a ≧ Tx then the approximate point spectrum and spectrum of T are cyclic subsets of the complex plane. That is, if α = |α|γ lies in one of these sets then so does |α|γk for all integers k.
On a sheaf representation of a class of near-rings
Authors: Szeto George 
Published: April 2009

AbstractIt is proved that R is a near-ring with identity in which every element is a power of itself if and only if it is isomorphic with a near-ring of sections of a sheaf of near-fields in which every element is a power of itself. We also obtain that the Boolean spectrum is homeomorphic with the space of all completely prime ideals of R with the Zariski topology.
Abstract harmonic analysis of generalised functions on locally compact semigroups with applications to invariant means
Authors: Wong James C. S. 
Published: April 2009

AbstractLet S be a locally compact semigroup and M(S) its measure algebra. It is shown that the dual M(S)* is isometrically order isomorphic to the space GL(S) of all generalised functions on S first introduced by Šreǐder (1950). Moreover, convolutions of elements in each of the spaces M(S)* and GL(S) can be defined in such a way that the above isomorphism preserves convolutions. These results on representation of functionals in M(S)* by generalised functions practically open up a new chapter in abstract harmonic analysis. As an example, some applications to invariant means on locally compact semigroups are given.
Linearization of certain uniform homeomorphisms
Authors: Weston Anthony 
Published: April 2009

AbstractThis article concerns the uniform classification of infinite dimensional real topological vector spaces. We examine a recently isolated linearization procedure for uniform homeomorphisms of the form φ: X →Y, where X is a Banach space with non-trivial type and Y is any topological vector space. For such a uniform homeomorphism φ, we show that Y must be normable and have the same supremal type as X. That Y is normable generalizes theorems of Bessaga and Enflo. This aspect of the theory determines new examples of uniform non-equivalence. That supremal type is a uniform invariant for Banach spaces is essentially due to Ribe. Our linearization approach gives an interesting new proof of Ribe's result.
Fourier algebra of a hypergroup. I
Authors: Muruganandam Varadharajan 
Published: April 2009

AbstractIn this article we study the Fourier space of a general hypergroup and its multipliers. The main result of this paper characterizes commutative hypergroups whose Fourier space forms a Banach algebra under pointwise product with an equivalent norm. Among those hypergroups whose Fourier space forms a Banach algebra, we identify a subclass for which the Gelfand spectrum of the Fourier algebra is equal to the underlying hypergroup. This subclass includes for instance, Jacobi hypergroups, Bessel-Kingman hypergroups.
A note on local polynomial functions on commutative semigroups
Authors: Grossman P. A. 
Published: April 2009

AbstractGiven a universal algebra A, one can define for each positive integer n the set of functions on A which can be “interpolated” at any n elements of A by a polynomial function on A. These sets form a chain with respect to inclusion. It is known for several varieties that many of these sets coincide for all algebras A in the variety. We show here that, in contrast with these results, the coincident sets in the chain can to a large extent be specified arbitrarily by suitably choosing A from the variety of commutative semigroups.
Groups fixing graphas in switching classes
Authors: Liebeck Martin W. 
Published: April 2009

AbstractA permutation group G on a finite set Ω is always exposable if whenever G stabilises a switching class of graphs on Ω, G fixes a graph in the switching class. Here we consider the problem: given a finite group G, which permutation representations of G are always exposable? We present solutions to the problem for (i) 2-generator abelian groups, (ii) all abelian groups in semiregular representations. (iii) generalised quaternion groups and (iv) some representations of the symmetric group Sn.
On bisimple semigroups generated by a finite number of idempotents
Authors: Byleen Karl 
Published: April 2009

AbstractNon-completely simple bisimple semigroups S which are generated by a finite number of idempotents are studied by means of Rees matrix semigroups over local submonoids eSe, e = e2 ∈ S. If under the natural partial order on the set Es of idempotents of such a semigroup S the sets ω(e) = {ƒ ∈ Es: ƒ ≤ e} for each e ∈ Es are well-ordered, then S is shown to contain a subsemigroup isomorphic to Sp4, the fundamental four-spiral semigroup. A non-completely simple hisimple semigroup is constructed which is generated by 5 idempotents but which does not contain a subsemigroup isomorphic to Sp4.
Invariant subspace lattices of Lambert's weighted shifts
Authors: Yadav B. S. , Chatterjee S. 
Published: April 2009

AbstractLet B(H) be the Banach algebra of all (bounded linear) operators on an infinite-dimensional separable complex Hilbert space H and let be a bounded sequence of positive real numbers. For a given injective operator A in B(H) and a non-zero vector f in H, we put We define a weighted shift Tw with the weight sequence on the Hilbert space 12 of all square-summable complex sequences by . The main object of this paper is to characterize the invariant subspace lattice of Tw under various nice conditions on the operator A and the sequence .
The Universality of the variety of quasigroups
Authors: Pigozzi Don 
Published: April 2009

AbstractThe variety of quasigroups is universal for varieties of algebras of the most general kind in the sense that each such variety can be interpreted in a natural way in a suitably chosen subvariety of quasigroups. More precisely, for any algebra〈A, f0, f1, f2, …〉wheref0, f1, f2, …is an arbitrary finite or infinite sequence of operations of finite rank, there exists a quasigroup 〈B,.〉 and polynormial operationsF0, F1, F2, … over 〈B,·〉 such that〈A, f0, f1, …〉is a subalgebra of〈B, F0, F1, …〉satisfying exactly the same identities. Moreover, if there are only finitely many f0, f1, …, then 〈B1〉 can be taken so that its identities are recursive in those of 〈A, f0, f1, …〉, If 〈A, f0, f1, …〉is a free algebra with an infinite number of free generators, thenBcan also be taken to coincide withA. This universal property of quasigroups has a number of consequences for their equational metatheory.
Upper radicals and essential ideals
Authors: Olson Dwight M. , Jenkins Terry L. 
Published: April 2009

AbstractFor any class of rings it is shown that the class (M) of all rings each nonzero homomorphic image of which contains either a nonzero -ideal or an essential ideal is a radical class. If is a class of simple rings the upper radical generated by , (M), is shown to be equal to (M) where ' is the class of simple rings complementary to .
Applications of p-adic interpolation to exponential polynomials and sums of powers
Authors: Laohakosol Vichian , Pitman Jane 
Published: April 2009

AbstractAn approach to p-adic interpolation via divided differences is used to give alternative proofs of results of van der Poorten on p-adic exponential polynomials and to derive a p-adic analogue of Turan's first main theorem on sums of powers.
Subgroups of HNN groups
Authors: Cohen D. E. 
Published: April 2009

The purpose of this paper is to give a more precise form of Theorem 1 of [2], which gives a structure theorem for subgroups of HNN groups; we prove the following.Let H be a subgroup of the HNN group <A, xi;xiU-ixi-1 = Ui>. Then H is an HNN group whose base is a tree product of groups H ∪ wAw-1 where w runs over a set of double coset representatives of (H,A); the amalgamated and associated subgroups are all of the form H ∊ vUiv-l for some v. We can be more precise about which subgroups occur and about the tree product. We will also obtain stronger forms of other results in [1] and [2].
Directed packings of pairs into quadruples
Authors: Skillicorn David B. 
Published: April 2009

AbstractA directed packing of pairs into quadruples is a collection of 4-subsets of a set of cardinality ν with the property that each ordered pair of elements appears at most once in a 4-subset (or block). The maximal number of blocks with this property is denoted by DD(2, 4, ν). Such a directed packing may also be thought of as a packing of transtivie tournaments into the complete directed graph on ν points. It is shown that, for all but a finite number of values of ν, DD(2, 4, ν) is maximal.
Equidistant permutation arrays: a bound
Authors: Van Rees G. H. J. , Vanstone S. A. 
Published: April 2009

AbstractAn equidistant permutation array is a ν × r array A(r, λ;ν) defined on a r-set X such that every row of A is a permutation of X and any two distinct rows agree in precisely λ common columns. Define In this paper, we show that where n = r − λ. Certain results pertaining to irreducible equidistant permutation arrays are also established.
Mesures coniques et intégrale de Daniell
Authors: Becker Richard 
Published: April 2009

AbstractLet X be a weakly complete proper cone contained in a weak space E and h(E) the Riesz space generated by the continuous linear forms on E. A positive conical measure μ on X is a positive linear form on h(E)|x. G. Choquet has proved μ is a Daniell integral on E when E is weakly complete, but μ is not generally a Daniell integral on X. However we give an integration theory for functions on X and compare this theory with the classical Daniell theory. The case where μ is maximal in the sense of G. Choquet is remarkable.
Higher order elliptic boundary value problems in spaces with homogeneous norms
Authors: Pryde A. J. 
Published: April 2009

AbstractWe consider general boundary value problems for homogeneous elliptic partial differential operators with constant coefficients. Under natural conditions on the operators, these problems give rise to isomorphisms between the appropriate spaces with homogeneous norms. We also consider operators which are not properly elliptic and boundary systems which do not satisfy the complementing condition and determine when they give rise to left or right invertible operators. A priori inequalities and regularity results for the corresponding boundary value problems in Sobolev spaces are then readily obtained.
A generalization of convex functions via support properties
Authors: Ben-Tal Aharon , Ben-Israel Adi 
Published: April 2009

AbstractWith respect to a given family of functionsF, a function is said to beF-convex, if it is supported, at each point, by some member ofF. For particular choices ofFone obtains the convex functions and the generalized convex functions in the sense of Beckenbach.F-convex functions are characterized and studied, retaining some essential results of classical convexity.
Homogeneous graphs and stability
Authors: Gardiner A. 
Published: April 2009

AbstractLet Γ be a graph with finite vertex set V. Γ is homogeneous if whenever U1, U2 ⊆ V are such that the vertex subgraphs (U1), (U2) are isomorphic, then every isomorphism from (U1) to (U2) extends to an automorphism of Γ; homogeneous graphs were studied by Sheehan (1974) and were classified by the author. Γ is locally homogeneous if whenever U ⊆ V, then every automorphism of (U) extends to an automorphism of Γ. We prove that every locally homogeneous graph is homogeneous.
The dilogarithm in algebraic fields
Authors: Lewin L. 
Published: April 2009

AbstractSpecial numerical formulae for the dilogarithm of powers of a base quantity have been shown to exist by Watson, Coxeter and others. Abel's equation for the dilogarithm was put in this “exponent” form, as a result of which a four-variable, symmetrical equation, also in exponent form, was deduced. From these equations a large number of special numerical results were produced, from which certain properties of a general structural nature emerged, and enabled two new results to be predicted.The algebraic bases for these results can be grouped in trigonometric or non-trigonometric form, and for the former it seems to be necessary to examine the properties of the dilogarithm in the complex plane. Even so, there are some identities that seem to be outside the scope of the present methods.It is speculated that certain factorization relations, which can be identified from the equations, may play a substantial role in the results; but so far no analytic derivation of this property has appeared possible.
Essential ideals, homomorphically closed classes and their radicals
Authors: Jenkins T. L. , le Roux H. J. 
Published: April 2009

AbstractOlson and Jenkins defined E(M) to be the class of all rings each nonzero homomorphic image of which contains either a nonzero M-ideal or an essential ideal where M, is any class of rings. E(M) was proven to be a radical class and various classes M were considered. Here the class E(M) is partitioned into two classes: H the class of all rings each nonzero homomorphic image of which has a proper essential ideal and the class H(M) of all rings each nonzero homomorphic image of which contains an M-ideal. It is shown that H is a radical class and under certain conditions H(M) is also a radical class. Various properties placed on M yield several well-known radical classes and an infinite number of supernilpotent nonspecial radical classes is constructed.
When is the algebra of regular sets for a finitely additive borel measure a α-algebra?
Authors: Armstrong Thomas E. 
Published: April 2009

AbstractIt is shown that hte algebra of regular sets for a finitely additive Borel measure μ on a compact Hausdroff space is a σ-algebra only if it includes the Baire algebra and μ is countably additive onthe σ-algebra of regular sets. Any infinite compact Hausdroff space admits a finitely additive Borel measure whose algebra of regular sets is not a σ-algebra. Although a finitely additive measure with a σ-algebra of regular sets is countably additive on the Baire σ-algebra there are examples of finitely additive extensions of countably additive Baire measures whose regular algebra is not a σ-algebra. We examine the particular case of extensions of Dirac measures. In this context it is shown that all extensions of a {0, 1}-valued countably additive measure from a σ-algebra to a larger σ-algebra are countably additive if and only if the convex set of these extensions is a finite dimensional simplex.
Embedding categories with exactness into their abelianization
Authors: Adelman Murray 
Published: April 2009

AbstractWe give a partial answer to the following questions: Given an additive category and a class of sequences, under what conditions is the universal functor to the abelian category faithful and what other sequences are taken to exact sequences?The “answers” to these questions appear as theorems 2.2 and 3.2 respectively and amount to a weakening of the condition that there be enough relative projectives.We then characterize those additive categories with exactness which have the property that all relative exact sequences are determined by a small set of functors into the category of abelian groups.
A new proof of the absence of limit cycles in a quadratic autonomous system
Authors: Matlak R. F. 
Published: April 2009

AbstractThe absence of limit cycles in the system (S): x′ = − y + dx2 + exy + fy2, y′ = x, (′ ≡ d/dt), for 0 ≦ f2 < 2, was shown by Yeh et al. (1963). The general case was established by Kukles and Šakhova using various special results and relying on an extraneous auxiliary system. In this paper we give a new proof of the theorem; in it, we draw mainly on the basic properties of the characteristic exponent of a cycle and use an intrinsic system, viz. the case d = − f(≠ 0) of (S) as an auxiliary system.
Promonoidal functor categories
Authors: Day B. J. 
Published: April 2009

AbstractIn this article a completion process for promonoidal categories is used to determine a sufficient condition for the existence of a promonoidal convolution structure on the category of functors between two promonoidal categories. This, in turn, leads to a partial closed structure on the 2-category of promonoidal categories, promonoidal functors, and promonoidal natural transformations.
Sylow subgroups of transitive permutation groups II
Authors: Praeger Cheryl E. 
Published: April 2009

AbstractLet G be a transitive permutation group on a finite set of n points, and let P be a Sylow p-subgroup of G for some prime p dividing |G|. We are concerned with finding a bound for the number f of points of the set fixed by P. Of all the orbits of P of length greater than one, suppose that the ones of minimal length have length q, and suppose that there are k orbits of P of length q. We show that f ≦ kp − ip(n), where ip(n) is the integer satisfying 1 ≦ ip(n) ≦ p and n + ip(n) ≡ 0(mod p). This is a generalisation of a bound found by Marcel Herzog and the author, and this new bound is better whenever P has an orbit of length greater than the minimal length q.
Extensions of semi-hereditary rings
Authors: Evans M. W. 
Published: April 2009

AbstractHattori (1960) defined a right R-module A to be torsion-free if for all a ∈ A and x ∈ R, ax = 0 implies that there exist elements {x1, x2, …, xn} ⊆ R with xix = 0 for all 1 ≦ i ≦ n and {a1, a2, …, an} ⊆ A such that a = aixi. Left torsion-free is defined similarly. It is shown that for a ring R, these torsion-free modules are the torsion-free class of a hereditary torsion theory, corresponding to a perfect topology, if and only if the left flat epimorphic hull of R is a regular ring which is both left and right torsion-free. A class of right semi-hereditary rings for which the torsion-free modules of Hattori satisfy the above property are found and this class of rings is discussed.