On maximal submodules of a finite direct sum of hollow modules. II (Q795903)

This paper is a sequel to the above one. The same conditions are presupposed for the rings. The above condition (ii) now implies that every maximal submodule of a direct sum of \(t+1\)-copies of a hollow module with length t contains a direct summand. It is this property now, which is studied for right artinian rings R with \(J^ 2=0\). In the first section of this paper the author gives results similar to those obtained in the foregoing paper. Now let R be either a commutative and local artinian ring or a local algebra of finite dimension over an algebraically closed field. Let \({\mathbb{N}}\) be a set of representatives of the isomorphism classes of serial modules with length two. The author proves that in both cases: (a) all \(N_ 1\oplus N_ 2\oplus...\oplus N_ n (N_ i\in {\mathbb{N}})\) satisfy the property of this paper and (b) R is a serial ring - are closely related.