奇异变换半群的局部极大幂等元生成子半群的结构(英文)

The structure of some locally maximal idempotent-generated subsemigroups of Sing n

设S是集合X ={ 1,2 ,… ,n}上的奇异变换半群 ,E是S的亏数为 1的全体幂等元之集 ,I是E的非空子集 ,所谓由I生成的子半群 I 是S的局部极大幂等元生成的子半群 ,即指 I 是S的真子半群 ,且对任何e∈E \ I ,有 I∪{e} =S。确定了S的所有局部极大幂等元生成子半群的结构 (在同构的意义下 )

Let Sing n be the semigroup consisting of all singular transformations on the set X n=｛1,2,…,n｝,and E the set of all idempotents of Sing, with defect one,I a subset of E. The generated subsemigroup ?I? is a locally maximal idempotent-generated subsemigroup of Sing n provided that ?I?≠Sing n but ?I∪｛e｝?=Sing n for each e∈E\?I?.The purpose of this paper is to determine the structure of all distinct (up to isomorphism) locally maximal idempotentgenerated subsemigroups of Sing n.