具有完全正则自同态半群的分裂图

本文给出了具有完全正则自同态半群的分裂图的结构特征．其证明方法有望应用于其他图族自同态半群的正则性及完全正则性的研究．     

图的字典序积和自同态幺半群

Ｆ．Ｈａｒａｒｙ￣［１］和Ｇ．Ｓａｂｉｄｕｓｓｉ￣［２］考虑过图Ｘ和ｙ的字典序积Ｘ［Ｙ］的自同构群ＡｕｔＸ［Ｙ］与它们各自的自同构群的圈积ＡｕｔＸ［ＡｕｔＹ］的关系，并给出了两者相等的一种刻划．在本文，我们考虑更广意义上的问题，即Ｘ［Ｙ］的自同态幺半群ＥｎｄＸ［Ｙ］与各自的自同态幺半群的圈积ＥｎｄＸ［ＥｎｄＹ］的关系，也给出了两者相等的一种刻划，同时得到了下面结果：如果Ｘ和Ｙ都是不含Ｋ＿３导出子图的连通图，且其中之一图有奇数围长，那么ＥｎｄＸ［Ｙ］＝ＥｎｄＸ［ＥｎｄＹ］．     

图的强收缩核与图的强自同态幺半群的正则性

本文研究图及其强自同态幺半群．首先刻画了图的强自同态幺半群的正则元，然后给出了此幺半群正则的充要条件．这推广了［１］和［２］中关于有限图的强自同态幺半群正则的结果．     

幺半群的内射类及投射类刻画

类比于一般环上模的内射类,定义了幺半群上的S-系的内射类和投射类,并利用它们刻画了几类特殊的幺半群．证明了完全内射幺半群和完全拟内射幺半群是等价的．并且证明了对于标致幺半群S,它是完全投射的当且仅当它是完全拟投射的当且仅当它上面的投射S-系构成了一个投射类．     

Endomorphism of Abelian Groups as Modules over Their Endomorphism Rings

Mathematical Notes - For an Abelian group $$A$$ , viewed as a module over its endomorphism ring $$E(A)$$ , the near-ring $$mathcal{M}_{E(A)}(A)$$ of homogeneous mappings is defined as the set of...     

Atomic Commutative Monoids and Their Elasticity

We present some characterizations of properties related to factorization problems on finitely generated commutative monoids. We also give a series of algorithms for studying these problems from a presentation of a given commutative monoid.     

Garside Structures on Monoids with Quadratic Square-Free Relations

We show the intimate connection between various mathematical notions that are currently under active investigation: a class of Garside monoids, with a “nice” Garside element, certain monoids S with quadratic relations, whose monoidal algebra A = kSA= textbf{k}S has a Frobenius Koszul dual A ^! with regular socle, the monoids of skew-polynomial type (or equivalently, binomial skew-polynomial rings) which were introduced and studied by the author and in 1995 provided a new class of Noetherian Artin-Schelter regular domains, and the square-free set-theoretic solutions of the Yang-Baxter equation. There is a beautiful symmetry in these objects due to their nice combinatorial and algebraic properties.     

Some Results on Green''s Relations for Monoids Presented by Monadic String-Rewriting Systems

For finite monadic string-rewriting systems that are confluent and for finite special string-rewriting systems that are λ -confluent it is shown that the R -class and the L -class of a string can be characterized by a regular set of irreducible strings. It follows that for these systems the relation D is decidable. Actually it is shown that this relation is decidable in polynomial time.     

On Graphs Determined by Their Tutte Polynomials

We say that a graph G is T-unique if any other graph having the same Tutte polynomial as G is necessarily isomorphic to G. In this paper we show that several well-known families of graphs are T-unique: wheels, squares of cycles, complete multipartite graphs, ladders, Möbius ladders, and hypercubes. In order to prove these results, we show that several parameters of a graph, like the number of cycles of length 3, 4 and 5, and the edge-connectivity are determined by its Tutte polynomial.Research partially supported by projects BFM2001-2340 and by CUR Gen. Cat. 1999SGR00356Final version received: January 10, 2003     

On the Determinability of Mixed Abelian Groups by Their Endomorphism Semigroups

Mixed Abelian groups with isomorphic endomorphism semigroups are studied. In particular, the question of when the isomorphism of endomorphism semigroups of Abelian groups implies the isomorphism of the groups themselves is investigated.     

Modules Determined by Their Tops and First Syzygies

The purpose of this note is to give an elementary proof of the fact discovered by Bautista and Perez that for an Artin algebra a module without selfextension is determined by its top and its first syzygy.     

由圈长分布确定的偶图

阶为n的图G的圈长分布是序列(C1，C2，…，Cn)，其中ci是图G中长为i的圈数．本文得到如下结果：设A∈_E(Kn,r)，|A|≤1，且n≤r≤min{n 6，2n-3)，则G=Kn,r，r-A是由它的圈长分布确定的．     

Endofunctors of Set Determined by Their Object Map

Functors uniquely determined by their object map are called DVO functors. In this paper, we continue the research into DVO endofunctors of the category Set of all sets and maps as started by V. Trnková, R. El Bashir and A. Barkhudaryan. Two families of connected DVO functors containing an isomorphic copy of the identity functor Id are described.     

由子模格决定的准素模

本文主要给出以下定理C。设Ri(i=1,2)是MLPI环（即Ri是有位单元的结合环，且每个极大左理想必是主理想），元素Pi∈Ri使得RiPi是Ri的极大左理想，Mi是Pi－准素的Ri－模。则我们有以下定理C 设M1的终Goldie维数（＝min{P^n1M1的Goldie维数|n=0,1,2,…|}）≤3，如果有子模格同构f:L(M1)^~-L(M2)。则有逆向全射系{R1/R1P1^n(n∈N)；θ}与{R2／R2P2^n2(n∈N)；θ′n}之间的同构{ψn:R1/R1P^n1→R2/P2^2(n∈N),其中θn和θ′n(n∈N)是自然满同态，ψn(n∈N)是环同构。若令R^*1,R^*2分别是以上两逆向全射系的逆向极限环。则有环同构ψ：R^*1^~-R^*2和M1到M2的ψ－线性同的φ，φ诱导出f:fR1x=R2φ（x），任意x∈M1。易见：（1）当P1＝0＝P2，且M1是有限维向量空间时，由定理C即得射影几何的基本定理；（2）当R1＝Z＝R2，且P1和P2为素数时，由定理C即得Pi＝P2，从百得Baer关于交换p－群的相应结果。     

Involution Semigroups Are Not Globally Determined

The purpose of this paper is to present an example of nonisomorphic involution semigroups which are globally isomorphic, i.e. which have isomorphic power algebras (elements of which are the nonempty subsets of the original algebras). As an immediate consequence, we obtain that (involution) semirings are not globally determined. September 7, 1999     

Plane Domains Which Are Spectrally Determined

This paper studies the trace of the heat kernelZ(t) _j=1 exp ( _j t), where{ _j } are the eigenvalues of atwo-dimensional Dirichlet or Neumann Laplace operator. FromZ(t), a sequence of invariants (geometrical invariants)such as area, boundary measure, Euler characteristics, etc., can bedetermined. Using these invariants, the existence of the nondisk domainswhich are determined from the information of Dirichlet and Neumannspectrum, can be shown. In addition, we prove that the number of suchdomains is infinite (uncountable) and these domains are not similar eachother.     

Self-Small Abelian Groups as Modules over Their Endomorphism Rings

Abstract

The strongly essentially indecomposable self-small abelian groups, of finite torsion free rank, which are (almost-)projective as modules over their endomorphism rings are characterized.     

Non-Abelian Groups of Order 16 and Their Endomorphism Semigroups

We prove that any finite group of order 16 is determined by its endomorphism semigroup in the class of all groups. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 14, Algebra, 2004.