On pseudo valuation module and injectivity property

Abstract

In this paper; we study the relationship between two modules in module theory namely injective and pseudo valuation modules. We investigated that every module has three properties which are noetherian, cyclic and regular is pseudo valuation modules. Also, if R is an Artinian ring and E is finitely generated regular module, it implies that E is (P.V.M). We proved that for an R-module E, if R is a commutative ring with E is a Noetherian, Artinian and regular module, then E is P.V.M. Finally, some definitions and new results have introduced in this paper.

Subject Classification:

• 97H40
• 13C05

Keywords:

• Injective modules
• Pseudo valuation module
• Regular module
• Finitely generated module
• Cyclic module