Published January 1, 2016
| Version v1
Journal article
Open
Rings with each right ideal automorphism-invariant
- 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
Description
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.
Files
bib-43813d16-760f-437a-a19b-23a98f10a300.txt
Files
(161 Bytes)
| Name | Size | Download all |
|---|---|---|
|
md5:4204fd80b0b26b8cda6bd6bfb6e0bc6a
|
161 Bytes | Preview Download |