满足零因子性质的环  

Rings satisfying a zero-divisor property

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：《兰州大学学报（自然科学版）》2008年第6期91-95,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：甘肃省自然科学基金(3ZS061-A25-015);甘肃省教育厅科研项目(0601-21)资助.

摘　　要：研究满足零因子性质的幂级数McCoy环、相对于幺半群的McCoy环和相对于幺半群的Armen- dariz环.得到了若R是交换的幂级数McCoy环,则R[x],R[x,x^(-1)]是McCoy环.对于整域R和R-模N,证明了R⊕N是幂级数McCoy环当且仅当N是右幂级数McCoy R-模.对于幺半群M,证明了若(?)R_i是M-McCoy环,则每个环R_i是M-McCoy环.同时给出了R[M]是Armendariz环和R[x]是M-Armenda- riz环的充分条件.Power-series McCoy rings, McCoy rings and Armendariz rings related to a monoid satisfying a zero-divisor property were investigated. The results show that if a commutative ring R is power-serieswise McCoy, then R[x] and R[x, x^-1] are McCoy rings, and that R ＋ N is a power-serieswise McCoy ring if and only if N is a right power-serieswise McCoy R-module, where R is an integral domain and N is an R-module. For a monoid M, it is proved that if ∏（i∈I） R4 is an M-McCoy ring, then each ring Ri, i∈I, is M-McCoy. Furthermore, some sufficient conditions for R[M] to be Armendariz and R[x] to be M-Armendariz were obtained.

关 键 词：幂级数McCoy环 幂级数Armendariz环 M—McCoy环 M—Armendariz环 直积 零因子 

分 类 号：O153.3[理学—数学]