若干类E-反演半群及其同余

【作者】 戴毓；

【导师】 郑恒武；

【作者基本信息】 曲阜师范大学 ， 基础数学， 2004， 硕士

【摘要】 本文研究E-反演半群及其同余，共分五节。 第一节为引言部分。第二节引入本文涉及的基本概念和必要的预备知识，研究E-反演半群，并给出若干性质。然后引入两类新的E-反演半群，举例说明它们与E-反演E-半群的关系。 第三节研究E-反演E-半群。给出E-反演E-半群的特征性质，完善了其等价条件。然后研究E-反演E-半群中元素和其弱逆元乘积以及弱逆元集W(S)的若干性质，给出E-反演E-半群、E-稠密半群的等价条件。 第四节首先借助满足(Ω)条件的同余ρ刻画E-反演半群上的若干特殊同余，诸如，E-反演半群上的带同余，E-反演E-半群上的半格同余、带同余、纯正同余，E-稠密半群和E-反演E-中心半群上的半格同余、逆同余。然后借助Clifford同余刻画了E-反演E-半群上的带同余、E-稠密(E-反演E-中心)半群上的半格同余。最后刻画了E-稠密半群上的逆同余和E-反演E-中心半群上的Clifford同余。 第五节给出E-反演半群S上若干同余的等价刻画。规定关系 借助C关系和买关系给出E一稠密半群上幂等元分离同余、群同余、半格同余的等价刻画以及E一反演E一半群上群同余、带同余的等价刻画.借助下0关系得到满足(△)条件的E一反演E一半群上幂等元分离同余和群同余的等价刻画.更多还原

【Abstract】 In this thesis, some classes of E-inversive semigroups and some congruences are investigated.The first section is a brief introuduction. In the second section, some basic conceptions and preliminaries about E-inversive semigroups are introuduced and some properties of E-inversive semigroups are obtained. Two classes of new E-inversive semigroups, completely E-inversive semigroups and E-inversive E-center semigroups, are given. The relationships among completely E-inversive semigroups, E-inversive E-center semigroups and E-inversive E-semigroups are demonstrated by the following examples.In the third section, E-inversive E-semigroups are investigated. Some properties and equivalent terms of E-inversive E-semigroups are obtained. The equivalent conditions of E-inversive E-semigroups and E-dense semigroups are given, respectively.The fourth section is devoted to the characterizations of congruences on E-inversive semigroups. Firstly, some special congruences are obtained by a given congruence which satisfys condition (?), such as band congruences on E-inversive semigroups, semilattice congruences, band congruences, orthodox congruences on E-inversive E-semigroups, semilattice congruences, inverse congruences on E-dense semigroups and E-inversive E-center semigroups. Secondly, band congrueces on E-inversive E-semigroups and semilattice congruences on E-dense (E-inversive E-center) semigroups are characterized by a given Clifford congruence. Finally, inversecongruences on E-dense semigroups and Clifford congruences on E-inversive E-center semigroups are obtained, respectively.In the fifth section, some equivalent characterizations of special congruences on E-inversive semigroups are given. Define relations C, F, F0 byThe equivalent characterizations of some congruences are presented by relations C and F- idempotent-separating congruences, group congruences and semilattice congruences on E-dense semigroups, group congruences and band congruences on E-inversive E- semigroups. The equivalent characterizations of idempotent-separating congruences and group congruences on E-inversive E-semigroups satisfy condition (A) are obtianed by the relation F0, respectively.更多还原