斜广义幂级数环的幂零性质(英文)  

Nilpotent Property of Skew Generalized Power Series Rings

作　　者：欧阳伦群[1] 刘金旺[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭湖南411201

出　　处：《数学进展》2013年第6期782-794,共13页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10771058,No.11071062);Natural Science Foundation of Hunan Province(No.10jj3065);Scientific Research Foundation of Hunan Provincial Education Department(No.10A033)

摘　　要：设R是NI环且nil(R)为幂零理想,(S,≤)为严格全序幺半群且对任意8∈S,s≥0,ω:S→End(R)为compatible幺半群同态.本文证明了斜广义幂级数环[[R^(S,≤),ω]]是幂零p.p.环当且仅当环R是幂零P.P.环.同时还进一步证明了如果环R对弱零化子满足降链条件,则斜广义幂级数环[R^(S,≤),ω]]是弱APP环当且仅当环R是弱APP环.因此基环R的许多性质可以推广到斜广义幂级数环[[R^(S,≤),ω]上.Let R be an NI ring with nil（R） nilpotent, （S, ≤） a strictly totally ordered monoid satisfying the condition that 0≤s for all s G S, andω ： S →End（R） be a compatible monoid homomorphism. Then the ring [[Rs,≤, ω]] of the skew generalized power series with coefficients in R and exponents in S is a nilpotent p.p.-ring if and only if R is a nilpotent p.p.-ring. Furthermore, if R satisfies the descending chain condition on weak annihilators, then [[RS＇≤, ω]] is a weak APP-ring if and only if R is a weak APP-ring. Consequently, some properties of the base ring R can be profitably generalized to the skew generalized power series ring [[Rs＇≤, ω]].

关 键 词：弱零化子 弱APP环 斜广义幂级数环 

分 类 号：O153.3[理学—数学]