Abstract :
In this paper, we study rings having the property that every right ideal is auto-morphism-invariant. Such rings are called right a-rings. It is shown that (1)aright a-ring is a direct sum of a square-full semisimple artinian ring and a right square-free ring, (2) a ring Ris 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)aright a-ring is von Neumann regular if and only if it is semiprime, and (5)aprime 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.
