项目名称: 若干类广义正则半群代数结构的研究
项目编号: No.11501331
项目类型: 青年科学基金项目
立项/批准年度: 2016
项目学科: 数理科学和化学
项目作者: 王艳慧
作者单位: 山东科技大学
项目金额: 18万元
中文摘要: 半群理论是代数学的一个重要研究领域。它在信息科学、自动机理论、形式语言等领域有着广泛的应用背景。本课题的研究内容主要为:①弄清包括富足半群和弱U-富足半群在内的广义正则半群上的广义格林关系、幂等元、富足元、弱U-富足元之间的关系,建立这些半群的基本半群,进而刻画这些半群的代数结构;②分别给出富足半群上的最小好同余和弱U-富足半群上的最小允许同余的精细刻画,构造与这些半群同构的P-半群,研究它们的嵌入问题;③利用图论中的树研究弱U-富足半群及其若干子类的代数结构。
中文关键词: 半群;广义正则半群;代数结构;P-半群;基本半群
英文摘要: The semigroup theory is an important research area of algebra. It has wide applications in many areas such as information science, automata theory and formal language. The main researches of this project are as follows. ① The relationship among generalised Green’s relations, idempotents, abundnant elements and weakly U-abundant elements on generlaised regular semigroups including abundant semigroups and weakly U-abundant semigroups will be explored; fundamental semigroups and algebraic structures of generalised regular semigroups will be characterised. ② This program will find the smallest good congruences on abundant semigroups and the smallest admissible congruences on weakly U-abundant semigroup to build P-semigroups, which are isomorphic to abundant or weakly U-abundant semigroups, and study their embedding problems. ③ The algebraic structures of weakly U-abundnant semigroups and its subclasses will be investigated in terms of trees.
英文关键词: semigroups;generalised regular semigroups;algebraic structures;P-semigroups;fundamental semigroups