关于在π—逆半群的H^＊关系

A NOTE ON H~*-RELATION OF LEFT π-INVERSE SEMIGROUP

研究一类特殊的左π—逆半群S ,即满足条件RegS≤S的左π—逆半群 .证明了H —关系是左r—半素同余的充要条件是ea =eae, e∈E(S) , a∈Gr(S) ,且r(ab)q - 1 r(a)r(b) , a ,b∈S .以前的有关结果即为该结论的推论 .

This paper discussed a special kind of left π-inverse semigroup,which satisfies the condition of RegS≤S,proved the recessary and sufficiend conditions of H*-relation is left r-semiprime congruence relation,namely,ea=eae,e∈E(S),a∈Gr(S),and r(ab) H*r(a)r(b),a,b∈S.THen the results of [1]and[2] become into the papers corollary.