相对于幺半群的拟-McCoy环  

Quasi-McCoy rings relative to a monoid

作　　者：杨世洲[1] 宋雪梅[2] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070 [2]兰州城市学院数学学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2010年第8期47-52,56,共7页Journal of Shandong University(Natural Science)

基　　金：甘肃省自然科学基金资助项目(3ZS061-A25-015)

摘　　要：引入了M-拟-McCoy环并研究了其性质。对u.p.幺半群M,证明了reversible环是M-拟-McCoy环。对于包含无限循环子幺半群的交换可消幺半群M及u.p.幺半群N,若R是交换的M-拟-McCoy环,则R[N]是M-拟-Mc-Coy环及R是M×N-拟-McCoy环。对幺半群M,R是M-拟-McCoy环当且仅当上三角矩阵环Tn(R)是M-拟-Mc-Coy环及直积∏i∈IRi是M-拟-McCoy环当且仅当每个Ri(i∈I)是M-拟-McCoy环。M-quasi-McCoy rings are introduced,and their properties are investigated.It is shown that,for any unique product monoid M,every reversible ring is M-quasi-McCoy.If M is a commutative and cancellative monoid containing an infinite cyclic submonoid,N is a u.p.monoid and R is a commutative M-quasi-McCoy ring,then R[N] is M-quasi-McCoy and R is M×N-quasi-McCoy.For a monoid M,R is a M-quasi-McCoy ring if and only if the upper triangular matrix ring Tn（R）is a M-quasi-McCoy ring and direct product ∏i∈IRi is a M-quasi-McCoy ring if and only if each ring Ri（i∈I）is a M-quasi-McCoy ring.

关 键 词：幺半群 u.p.幺半群 M-拟-McCoy环 M-拟-Armendariz环 上三角矩阵环 直积 

分 类 号：O153.3[理学—数学]