On endomorphism rings of automorphism-invariant modules

Abstract. In this paper, we give some results of endomorphism rings of automorphism-invariant modules. It shows that if \(M\) is an automorphism-invariant self-generator module with finite Goldie dimension then every maximal left ideal of \(End(M)\) has the form \(A_u\) for some right uniform element \(u\) in \(End(M)\). We also show that a ring \(R\) is right self-injective if and only if \(R\) is right automorphism-invariant and \(R_R\) is weakly injective. Finally, we obtain a decomposition of finite Goldie dimension right automorphism-invariant rings.