On semiperfect a -rings

Abstract

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.