关于R-左消幺半群

ON R-LEFT CANCELLATIVE MONOIDS

引入了半群S上的等价关系L^ ,证明了半群S是R -左消幺半群的拟膨胀当且仅当S是L^ -单的 ,且含有中心幂等元 ;证明了半群S是左零带和R -左消幺半群的直积的拟膨胀当且仅当S是L^ -单的左E -完全半群 ,且对任意a∈S ,存在唯一的幂等元e使得对任意b∈S2 都有ab =eab .

The equivalent relation on a semigroup is given.We show that a semigroup S is a quasi-inflation of an R-left cancellative monoid if and only if S is an LΔ-simple semigroup,and contains a central idempotent.Moreover,We prove that a semigroup S is a quasi-inflation of direct product of a left zero band and an R-left cancellative monoid if and only if S is an LΔ-simple semigroup,and a left E-full semigroup and for each a in S there exists an idempotent e such that ab=eab,where b is any element of S2.