全子半群构成链的正则半群

摘要

半群S的子半群定义为全子半群,若S的所有幂等包含在子半群中.通过研究正则半群的全子半群格,得到了正则半群的全子半群格构成链的一个充分必要条件.并且推广出一类特殊的正则半群,纯正半群的全子半群格构成链的一个充分必要条件.进而得到纯正半群S的全子半群格构成链,当且仅当正则半群S的全正则子半群格构成链.%The definition of semigroup of semigroup S is complete semigroup if all powers of S are includ-ed in the sub-semigroup.This paper realized a necessary and sufficient condition for the dynamic combina-tion of lattice of full sub-semigroups of regular semigroup by studying lattice of full sub-semigroups of reg-ular semigroup.And it generalized one special class of regular semigroup,a necessary and sufficient condi-tion of lattice of full sub-semigroups dynamic combination of orthodox semigroup.Then lattice of full sub-semigroups dynamic combination of orthodox semigroup S was realized when and only when lattice of full sub-semigroups dynamic combination of regular semigroup S is.