弱GPP-环的Ore扩张  

Ore extensions of weakly GPP-rings

作　　者：杨晓燕[1] 刘仲奎[1] 

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

出　　处：《西北师范大学学报（自然科学版）》2005年第3期19-21,共3页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金(10171082)资助项目

摘　　要：设α是一个自同态,δ是环R的α微分.如果R是α刚性环,则R是弱GPP环当且仅当R[x;α,δ]是弱GPP环.设R是α刚性环,R[[x;α]]是PP环当且仅当R是PP环,且R的任意可数幂等元集在I(R)中有广义join.Let α be an endomorphism and δ be an α-derivation of a ring R.Assume that R is an α-rigid ring,then R is a weakly GPP-ring if and only if the Ore extension R[x;α;δ] is a weakly GPP ring. Let R be an α-rigid ring,the skew power series ring R [[x;α]] is a PP-ring if and only if R is a PP-ring and any countable family of idem potents of R has a generalized join in I(R).

关 键 词：α-刚性环 弱GPP-环 PP-环 

分 类 号：O153.3[理学—数学]