Article ID Journal Published Year Pages File Type
6415831 Journal of Pure and Applied Algebra 2016 13 Pages PDF
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 Mn(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.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
Authors
, , ,