D-半群上的拓扑

Topology on D-semigroups

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.