一般半群和广义正则半群的代数理论

项目名称： 一般半群和广义正则半群的代数理论

项目编号： No.11471255

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 任学明

作者单位： 西安建筑科技大学

项目金额： 70万元

中文摘要： 半群代数理论是代数学的重要分支之一。半群代数理论在〝形式语言〞、〝理论计算机科学〞和〝信息科学〞等领域有着深厚的背景和广泛的应用。 本课题的研究内容主要为①研究广义正则半群及其若干子类的代数结构，刻画这些半群上的任意同余，特别地探讨具弱PC条件和具正则性条件的富足半群的代数理论；②弄清主右投射(rpp)半群中幂等元、正则元与广义格林关系的内在联系，建立若干主右投射半群的代数结构；③研究U-半富足半群的代数结构、序结构、同余理论及簇理论，给出这些半群上的允许同余和允许同余对的一个精细刻画，得到U-半富足半群的一个分类；④ 研究广义正则半群理论在半群字和形式语言（特别地，编码）方面的应用；⑤ 研究幂等生成半群的富足性及其它们的构造问题。

中文关键词： 半群；广义正则半群；代数结构；同余理论；半群簇

英文摘要： The algebraic theory of semigroups is one of important branches of algebra. The algebraic theory of semigroups has deep theoretical background and widely applications in many areas, such as Formal Languageand Theoretical Computer Science . The main researchs of this project are as follows: ① The algrbraic structures of several subclasses of generalised regular semigroups will be studied and arbitrary congruences on those semigroups will be characterised, especially, the algebraic theory of abundant semigroups with the weakly PC condition and satisfying the regular condition will be investigated；② The relationship among idempotents, regular elements and generalised Green's relations on rpp semigroups will be explored and the algebraic structures of rpp semigroups will be established; ③The program will investigate the structures、 partial orders、 congruences and varieties for U-abundant semigroups, and will find out the descriptions of admissible congruences and pairs of admissible congruences on such semigroups; A classification of U-semiabundant semigroups will be explored；④ The program will find some applications of theory of generalised regular semigroups to the fields of the word problem for semigroups and language (specially, algebraic code)；⑤ The abundant properties and constructions of idempotents generated semigroups will be studied.

英文关键词： semigroups;generalized regular semigroups;algebraic structures;congruences;varieties