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.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
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.
