项目名称: 几类广义正则半群、作用和范畴及其在圈积和图中的应用
项目编号: No.11261018
项目类型: 地区科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 李春华
作者单位: 华东交通大学
项目金额: 45万元
中文摘要: 自上世纪70年代以来,广义正则半群一直是半群界研究的重要课题。本项目研究目前国际半群界极具吸引力的几类广义正则半群- - (有限)abundant半群(如type-B半群等)、弱(半)abundant半群及满足一定条件的E-可逆半群(如E-可逆abundant半群等),并研究其各种作用和范畴理论,且与其它交叉学科结合(如半群和图结合等),从而形成研究内容上的一大特色。具体为:(1)研究上述几类半群的结构、平移包,并通过引入一种新的核-迹法和U-V关系法来进行这类半群同余刻画等;(2)利用同调代数中范畴论研究含幺元的上述几类半群的各种作用(如部分序作用、平坦作用等)及幺半群范畴等;(3)研究上述几类幺半群在自动机理论中的圈积构造及在图中的应用(如利用相关幺半群作用和圈积来刻画与图有关的组合问题等)。以上研究不仅可极大地丰富半群代数理论,而且在同调代数、自动机理论、图论等领域有着重要的应用价值。
中文关键词: 广义正则半群;作用;范畴;圈积;图
英文摘要: Since the 1970s, the generalized regular semigroup always has been an important subject of the semigroup research. This project studies some attractive classes of generalized regular semigroups in the present international research field of semigroups- - ( finite )abundant semigroups ( for example, type B semigroups, etc ), weakly abundant semigroups, semi-abundant semigroups and E-inversive semigroups which satisfy some conditions ( for example, E-inversive abundant semigroups, etc ), and considers some acts and categories of them. Furthermore, we shall consider combining them with other cross-cutting disciplines( for example, a combination of semigroups and graphs, etc ) which will form a major feature of our research contents. The followings are specific contents: (1)study semigroup structures, translational hulls of the above semigroups, and give descriptions of semigroup congruences of such semigroups by using a new "Kernel-trace" method and a new "U-V relation" method; (2)study some acts ( for example, partially ordered acts, flat acts, etc ) and categories of the above semigroups with an identity element by using category theories in homological algebra; (3)consider wreath product constructions of the above monoids in algebraic automata theory, and study some applications of them in graph theory (
英文关键词: generalized regular semigroup;act;category;wreath product;graph