广义逆多项式模的Attached素理想

Attached Primes of Generalized Inverse Polynomial Modules

设R是有单位元1的结合环,(S,≤)是严格全序Artin幺半群,M_R是右R-模,Att(M_R)与Att([M^(S,≤)]_([[R^(S,≤)]]))分别表示模M_R与广义逆多项式模[M^(S,≤)]_([[R^(S,≤)]])的所有Attached素理想组成的集合.该文主要讨论了广义幂级数环[[R^(S;≤)]]广义逆多项式模[[R^(S;≤)]]的Attached素理想的相关性质,证明了在一定条件下,有Att([M^(S,≤)]_([[R^(S,≤)]])={[[PR^(S;≤)]]P∈Att(M_R)}.这一结论表明广义逆多项式模([M^(S,≤)]_([[R^(S,≤)]])的Attached素理想在一定条件下可以用模M_R的Attached素理想来刻画,推广了Annin S在文献[1]中关于斜多项式环上逆多项式模的Attached素理想的相关结论.

Let R be an associative ring with identity,and （S,≤） a strictly totally ordered monoid which is also artinian and MR a right R-module.Attached primes of a generalized inverse polynomial module [MS,≤] over a generalized power series ring [[RS,-≤]] are considered in this paper.Given a module MR,we write Att（MR） for the Attached primes of MR.It is shown that Att（[MS,≤][[RS,≤]]） ={[[PS,≤]] ｜ P ∈ Att（MR）} under some additional conditions.Thus all Attached primes of [MS,-≤][[RS,≤]] can be described in terms of the Attached primes of MR in a very straightforward way.This result partially generalizes the S.Annin＇s recent work [1] on inverse polynomial modules over skew polynomial rings.