Small monoform modules

Abstract EN

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.