D-半群上的拓扑  

Topology on D-semigroups

作　　者：潘芳芳[1] 曹文营 王顺钦[3] 

机构地区：[1]西安邮电大学理学院,陕西西安710121 [2]驻马店市第二初级中学,河南驻马店463000 [3]南阳师范学院数学与统计学院,河南南阳473061

出　　处：《南阳师范学院学报》2014年第9期1-3,21,共4页Journal of Nanyang Normal University

基　　金：国家自然科学基金资助项目(11001158);西安邮电大学青年教师科研基金项目(ZL2014-38);河南省基础与前沿技术研究计划项目(132300410477)

摘　　要：研究D-半群的结构性质.借助于Rees序,建立了D-半群范畴和序半群范畴之间的函子,并证明了幂等可换半群范畴ICSGr是D-半群范畴DSGr的余反射子范畴,同时,也研究了D-半群S上的右理想拓扑τS,证明了(S,τS)是T0-空间当且仅当S是幂等可换的半群,并且d=idS.The main purpose of this paper is to investigate the structure of D-semigroups, where D-semigroups may be viewed as generalizations of inverse semigroups. In terms of Rees order, we build a functor from the cate- gory of D-semigroups to the category of ordered semigroups, and prove that the category ICSGr of idempotent and commutative semigroups is a reflective subeategory of the category DSGr of D-semigroups. Furthermore, we also prove that for the right ideal topology τs on a D-semigroup S, （S, τs） is a T0-space if and only if S is an idempotent commutative semigroup and d = ids.

关 键 词：D-半群 Rees序 序半群 T0-空间 范畴 

分 类 号：O153.1[理学—数学]