On pseudo valuation module and injectivity property

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 g...

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Bibliographic Details
Published inJournal of discrete mathematical sciences & cryptography Vol. 25; no. 8; pp. 2753 - 2757
Main Authors Saleh, Amnah M., Abed, Majid Mohammed
Format Journal Article
LanguageEnglish
Published Taylor & Francis 17.11.2022
Subjects
Cyclic module
Finitely generated module
Injective modules
Pseudo valuation module
Regular module
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Summary: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.
ISSN:0972-0529
2169-0065
DOI:10.1080/09720529.2022.2060919