拟右半群及其特征

Quasi-right semigroups and their properties

半群S称为拟正则的,如果关于每一个元素a∈S,存在自然数n及元素x∈S使得an=an×an.半群S称为具左中心幂等元,如果关于任意x,y∈S1,y≠1,及任意幂等元e∈S,使得x∈y=e×y.具有左中心幂等元的正则半群和富足半群早在1999年已由岑嘉评和任学明研究.本文讨论具有左中心幂等元的拟正则半群及其代数性质.文中首先定义了拟右半群,证明了拟右半群为拟右群的半格,进而给出了拟右半群的若干代数特征.

A semigroup S is called quasiregular if for every element a in S there exists a natural n and an element x in S such as a^n=a^n×a^n. A semigroup with left central idempotents is a semigroup that may satisfiy x∈y=e×y for any x,y in S and any idempotent e in S. Regular semigroups and abundant semigroups both having left central idempotents have been investigated by Shum and Ren in 1999. Quasiregular semigroups with left central idempotents are studied in this paper. Definition is given to a quasi-right semigroup that a quasiregular semigroup with left central idempotents where the set of its all regular elements is an ideal of S. Such a semigroup is a semilattice of quasi-right groups. Also, some special features of quasi-right semigroups are given.