广义逆多项式模的Attached 素理想

数学物理学报 ›› 2014, Vol. 34 ›› Issue (3): 521-529.

广义逆多项式模的Attached 素理想

欧阳伦群|刘金旺

湖南科技大学 |数学与计算科学学院湖南湘潭 411201

收稿日期:2012-05-07 修回日期:2013-12-18 出版日期:2014-06-25 发布日期:2014-06-25
基金资助:
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

Attached Primes of Generalized Inverse Polynomial Modules

OUYANG Lun-Qun, LIU Jin-Wang

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

摘要/Abstract

摘要：

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^; ^≤]]上广义逆多项式模[M^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^, ^≤]]})={[[P^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.

关键词: Attached素理想, 广义幂级数环, 广义逆多项式模

Abstract:

Let R be an associative ring with identity, and (S, ≤) a strictly totally ordered monoid which is also artinian and M_R a right R-module. Attached primes of a generalized inverse polynomial module [M^S^, ^≤] over a generalized power series ring [[R^S^, ^≤]] are considered in this paper. Given a module M_R, we write Att(M_R) for the Attached primes of M_R. It is shown that Att([M^S^, ^≤]_[[R^S^,_≤_]])⁼[[P^S^, ^≤]]|P∈Att(M_R)} under some additional conditions. Thus all Attached primes of [M^S^, ^≤][[R^S^, ^≤]] can be described in terms of the Attached primes of M_R 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

中图分类号:

16B60

欧阳伦群, 刘金旺. 广义逆多项式模的Attached 素理想[J]. 数学物理学报, 2014, 34(3): 521-529.

OUYANG Lun-Qun, LIU Jin-Wang. Attached Primes of Generalized Inverse Polynomial Modules[J]. Acta mathematica scientia,Series A, 2014, 34(3): 521-529.