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UDC 512.5 A ring is called a right a -ring if every right ideal is automorphism invariant. We describe some properties of a -rings over semiperfect rings. It is shown that an I-finite right a -ring is a direct sum of a semisimple Artinian ring and a basic ring. It is also demonstrated that if R is an indecomposable (as a ring) I-finite right a -ring not simple with nontrivial idempotents such that every minimal right ideal is a right annihilator and S o c ( R R ) = S o c ( R R ) is essential in R R , then R is a quasi-Frobenius ring and it is also a right q -ring.
Van et al. (Wed,) studied this question.
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