Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415831 | Journal of Pure and Applied Algebra | 2016 | 13 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M. Tamer KoÅan, Truong Cong Quynh, Ashish K. Srivastava,