Rings whose every right ideal is a finite direct sum of automorphism-invariant right ideals

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 $\Sigma$-$a$-rings. We find a representation in the form of block upper triangular rings of formal matrices for the indecomposable right Artinian right hereditary right $\Sigma$-$a$-rings.