Rings with each right ideal automorphism-invariant

2015/03/08 by Koşan, M. Tamer, Quynh, Truong Cong, Srivastava, Ashish K. · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1503.02245

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 \mathbbM_n(R) for some n>1 is a right a-ring, (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.

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