Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals

Abstract

© 2020, Pleiades Publishing, Ltd. We study the rings R whose every right ideal is a finite direct sum of automorphism-invariant right R-modules. These rings are called right Σ-a-rings. We find a representation in the form of block upper triangular rings of formal matrices for the indecomposable right Artinian right hereditary right Σ-a-rings.