On Morita equivalent of indecomposable automorphism-invariant rings

Abstract

In this paper, we give some results of indecomposable rings in which finitely generated right ideals are automorphism-invariant. They are called [Formula: see text]-rings. It shows that any indecomposable right artinian right Rickart right [Formula: see text]-ring [Formula: see text] is Morita equivalent to a formal upper triangular matrix ring. Moreover, we also study endomorphism rings of automorphism-invariant modules.