Pure Maximal Submodules and Related Concepts

Authors

khawla ahmed Department of Mathematics, College of Science, University of Baghdad, Iraq
Nuhad S. Al. Mothafar Department of Mathematics, College of Science, University of Baghdad, Iraq

DOI:

https://doi.org/10.30526/36.4.3139

Keywords:

R-module, R-submodule, Pr-module, Pr-maximal,Pr-local, N-maximal.

Abstract

In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule of an R-module is called Pr- maximal if ,for any submodule of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule

of an R-module is named near (N-maximal) whensoever is pure submodule of such that then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of is Pr-maximal. A ring is named Pr-ring if whole proper ideal of is a Pr-maximal ideal, we offer the concept pure local (Pr-local) module an R-module is named pure local (Pr-local) module. If it has only a Pr-maximal submodule which includes all proper submodule of . A ring is named pure local (Pr-local) ring, if is a Pr-local R-module. We give some relatio among Pr-maximal submodules and others related concept.

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