Rings with each right ideal automorphism-invariant


Kosan M. T. , Truong Cong Quynh T. C. Q. , Srivastava A. K.

JOURNAL OF PURE AND APPLIED ALGEBRA, vol.220, no.4, pp.1525-1537, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 220 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1016/j.jpaa.2015.09.016
  • Title of Journal : JOURNAL OF PURE AND APPLIED ALGEBRA
  • Page Numbers: pp.1525-1537

Abstract

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.