Co-small monoform modules

Abstract

The concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom_R(V, U), implies that ker f is small submodule of V.  In this paper the author dualizes this concept; she calls it co-small monoform module.  Many fundamental properties of co-small monoform module are given.  Partial characterization of co-small monoform module is established.  Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi.  She shows that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules.  Furthermore, some subclasses of co-small monoform are investigated.  Other generalizations of co-small monoform are introduced.