A Note on an R-Modules with Nearly Pure Intersection Property

Authors

  • Nuhad S Al-Mothafar Department of Mathematic, Collage of Science, University of Baghdad.

Keywords:

Pure submodule, Nearly Pure submodule, module with the Nearly Pureintersection property

Abstract

Let R be a commutative ring with identity and let M be a left R–module. A submoduleN of an R-module M is said to be nearly pure of M (abbreviated by N- pure), if N⋂IM=IN+J(M)⋂(N⋂IM), for each ideal Iof R; where J(M) is the Jacobson radical of M. The main purpose of this paper is to introduce the concept of modules with the Nearly Pure intersection property, andwe show that if M=A⊕B, has the NPIP and f:A→B is an R-homomorphism for any N – pure submodules A and B, then kernel f is N-pure.

 

Published

2018-07-16

Issue

Section

Articles

How to Cite

(1)
A Note on an R-Modules With Nearly Pure Intersection Property. ANJS 2018, 16 (1), 171-175.