Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (3): 521-529.

• Articles • Previous Articles     Next Articles

Attached Primes of Generalized Inverse Polynomial Modules

 OUYANG Lun-Qun, LIU Jin-Wang   

  1. School of Mathematics and Statistics, Hunan University of Science and Technology, Hunan Xiangtan 411201
  • Received:2012-05-07 Revised:2013-12-18 Online:2014-06-25 Published:2014-06-25
  • Supported by:

    国家自然科学基金(11071062)、湖南省自然科学基金(10jj3065)和湖南省研究生教改项目(10A033)资助

Abstract:

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, ]]|PAtt(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.

Key words: Attached prime ideal, Generalized power series ring, Generalized inverse polynomial module

CLC Number: 

  • 16B60
Trendmd