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]].
出处
《数学进展》
CSCD
北大核心
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)
关键词
弱零化子
弱APP环
斜广义幂级数环
weak annihilator
weak APP-ring
skew generalized power series
