关于R-左消幺半群  

ON R-LEFT CANCELLATIVE MONOIDS

作　　者：杜兰[1] 

机构地区：[1]郑州大学系统科学与数学系,河南郑州450052

出　　处：《山东师范大学学报（自然科学版）》2003年第4期5-7,共3页Journal of Shandong Normal University(Natural Science)

基　　金：郑州大学博士后科学基金资助项目

摘　　要：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.

关 键 词：R-左消幺半群 拟膨胀 中心幂等元 C-RPP半群 左零带 

分 类 号：O152.7[理学—数学]