Characterizations of unique maximal submodule and strong m-system

Abstract

In this paper we have introduced the concept of strong m-system in modules over non-commutative rings. Using the strong m-system, the existence of unique maximal submodule is proved. In fact we have shown that if I is a submodule and S is a strong m-system with I∩S=∅ then there exists a unique maximal submodule P with I⊂P such that P∩S=∅. We have also obtained a characterization for unique maximal submodule.