强右C-wlpp半群

Strong Right C-wlpp Semigroups

称半群S是强右C-wlpp的,若a∈S,E(R**a)≠Φ且存在唯一a+∈E(R**a),a+a=a,进而x,y∈S,e∈E(S)有xey=xye,证明这类半群是C-wlpp半群和左正规带关于半格Y的织积,也是L右消半群Mα×Lα(α∈Y)的强半格Y,其中Mα是L-右消幺半群,Lα是左零半群.

A semigroup S is said to be strong right C-wlpp,if a∈ S,E（Ra^＊＊）≠Φ and there exists a unique a＋∈ E（Ra^＊＊）such that a＋a = a,moreover x,y∈S,e∈E（ S） the equation xey = xye is satisfied. In this paper it is proved that a semigroup S is strong right C-wlpp if and only if S is a spined product of a C-wlpp semigroup and a left normal band with respect to a semilattice,if and only if S is a strong semilattice of a family L-right cancellative semigroups { Mα× Lα｜ α∈ Y},where Mα（α∈Y） are L-right cancellative monoids and Lα（α∈Y） are left zero semigroups.