E-反演半群和E~*-稠密半群及其同余

【作者】 张玉芝；

【导师】 郑恒武；

【作者基本信息】 曲阜师范大学 ， 基础数学， 2008， 硕士

【摘要】 本文主要研究E-反演半群及E~*-稠密半群的若干性质和同余,全文共分五节。第一节是引言。第二节给出基本的概念和必要的预备知识,给出若干类特殊的E-反演半群及E~*-稠密半群的基本性质。第三节分两部分。第一部分得到E-反演半群及特殊E-反演半群的一些性质,并把正则半群的夹心集的一些性质推广到E-反演半群上。第二部分得到E~*-稠密半群的性质,并给出范的E~*-稠密E-半群的一个等价条件。第四节首先利用半群S上包含D关系的0-限制的同余刻画范的E~*-稠密E-半群上的0-限制的逆同余。然后利用满足(Ω)条件的同余刻画范的E~*-稠密E-半群上的0-限制的本原逆同余,范的完全E~*-稠密E-半群上的0-限制的带同余,以及范的完全E~*-稠密E-中心半群上的0-限制的半格同余。第五节首先给出特殊E-反演半群和E~*-稠密半群上的幂等元分离同余的等价刻画,最后,借助半群上的幂等元给出E-反演半群上最小群同余的等价刻画。更多还原

【Abstract】 In this paper,we mainly study certain properties and congruences of E-inversive semigroups and E~*-dense semigroups.It is composed of five sections.The first section is a brief introduction.In the second section,the basic concepts and necessary preliminaries are given.Basic properties of certain class of E-inversive semigroups and E~*-dense semigroups are investigated,respectively.In the third section,it is divided into two parts.In the first part,some properties of E-inversive semigroups and special E-inversive semigroups are obtained.Moreover,some properties about sandwich sets of regular semi-groups are extended to E-inversive semigroups.In the second part,we get some properties of E~*-dense semigroups.The equivalent condition of categorical E~*-dense E-semigroup is given.The fourth section is devoted to the characterizations of congruences on E~*-dense E-semigroups.Firstly,letρbe a O-restricted congruence on S containing D.Then we describe the O-restricted inverse congruence on categorical E~*-dense E-semigroups relying,onρ.Secondly,relying on a given congruence satisfying condition(Ω),we obtain some special congruences,such as the O-restricted inverse congruence on categorical E~*-dense E-semigroups,the O-restricted band congruence on completely categorical E~*-dense E-semigroups, the O-restricted semilattice congruence on completely categorical E~*-dense E-center semigroups.In the fifth section,we give some equivalent characterizations of idempotent-separating congruences on special E-inversive semigroups and E~*-dense semi-groups. The equivalent characterizations of the least group congruence on E-inversive semigroups are given.更多还原