Small Monoform Modules

Abstract

Let R be a commutative ring with unity, let M be a left R-module. In this paper we introduce the concept small monoform module as a generalization of monoform module. A module M is called small monoform if for each non zero submodule N of M and for each f ∈ Hom(N,M), f ≠0 implies ker f is small submodule in N. We give the fundamental properties of small monoform modules. Also we present some relationships between small monoform modules and some related modules

Keywords

• Monoform module, small monoform module, small submodule, prime module, small prime module, uniform module, non singular module, quasi-Dedekind module.