ON AUTOMORPHISM-INVARIANT MULTIPLICATION MODULES OVER A NONCOMMUTATIVE RING

被引:0
作者
Thuyet, Le Van [1 ]
Quynh, Truong Cong [2 ]
机构
[1] Hue Univ, Coll Educ, Dept Math, 34 Le Loi, Hue City, Vietnam
[2] Univ Danang, Univ Sci & Educ, Dept Math, 459 Ton Duc Thang, Danang City, Vietnam
来源
INTERNATIONAL ELECTRONIC JOURNAL OF ALGEBRA | 2024年 / 36卷
关键词
Automorphism-invariant module; duo ring; quasi-duo ring; mul- tiplication module; commutative multiplication of ideals;
D O I
10.24330/ieja.1411145
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
. One of the important classes of modules is the class of multiplication modules over a commutative ring. This topic has been considered by many authors and numerous results have been obtained in this area. After that, Tuganbaev also considered the multiplication module over a noncommutative ring. In this paper, we continue to consider the automorphism-invariance of multiplication modules over a noncommutative ring. We prove that if R is a right duo ring and M is a multiplication, finitely generated right R-module with a generating set {m1, ... , mn} such that r(mi) = 0 and [miR : M] subset of C(R) the center of R, then M is projective. Moreover, if R is a right duo, left quasi-duo, CMI ring and M is a multiplication, non-singular, automorphism-invariant, finitely generated right R-module with a generating set {m1, ... , mn} such that r(mi) = 0 and [miR : M] subset of C(R) the center of R, then MR similar to= R is injective.
引用
收藏
页码:73 / 88
页数:16
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