Rings with each right ideal automorphism-invariant

被引：21

作者：

Kosan, M. Tamer ^{[1
]}

Truong Cong Quynh ^{[2
]}

Srivastava, Ashish K. ^{[3
]}

机构：

[1] Gebze Tech Univ, Dept Math, TR-41400 Gebze, Turkey

[2] Danang Univ, Dept Math, Da Nang City, Vietnam

[3] St Louis Univ, Dept Math & Comp Sci, St Louis, MO 63103 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2016年 / 220卷 / 04期

关键词：

MODULES;

D O I：

10.1016/j.jpaa.2015.09.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study rings having the property that every right ideal is automorphism-invariant. Such rings are called right a-rings. It is shown that (1) a right a-ring is a direct sum of a square-full semisimple artinian ring and a right square-free ring, (2) a ring R is semisimple artinian if and only if the matrix ring M-n(R) is a right a-ring for some n > 1, (3) every right a-ring is stably-finite, (4) a right a-ring is von Neumann regular if and only if it is semiprime, and (5) a prime right a-ring is simple artinian. We also describe the structure of an indecomposable right artinian right non-singular right a-ring as a triangular matrix ring of certain block matrices. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：1525 / 1537

页数：13

共 37 条

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