McCoy modules and related modules over commutative rings

被引：14

作者：

Anderson, D. D. ^{[1
]}

Chun, Sangmin ^{[2
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Seoul Natl Univ, Dept Math, Seoul 151747, South Korea

来源：

COMMUNICATIONS IN ALGEBRA | 2017年 / 45卷 / 06期

关键词：

Arithmetical module; Armendariz module; dual McCoy module; Gaussian module; McCoy module; ARMENDARIZ RINGS;

D O I：

10.1080/00927872.2016.1233218

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a left R-module. Then M is a McCoy (resp., dual McCoy) module if for nonzero f (X) is an element of R[X] and m(X) is an element of M[X], f (X) m(X) = 0 implies there exists a nonzero r is an element of R (resp., m is an element of M) with rm(X) = 0 (resp., f (X) m = 0). We show that for R commutative every R-module is dual McCoy, but give an example of a non-McCoy module. A number of other results concerning (dual) McCoy modules as well as arithmetical, Gaussian, and Armendariz modules are given.

引用

页码：2593 / 2601

页数：9