Weakly Primary Submodules over Non-commutative Rings

Ashour, Arwa and Hamoda, Mohammad (2016) Weakly Primary Submodules over Non-commutative Rings. Journal of Progressive Research in Mathematics(JPRM), 7 (1). pp. 917-927. ISSN ISSN: 2395-0218

[img]
Preview
Text
Hamoda+Ashour.pdf

Download (659kB) | Preview

Abstract

Let R be an associative ring with nonzero identity and let M be a unitary left R −module. In this paper, we introduce the concept of weakly primary submodules of M and give some basic properties of these classes of submodules. Several results on weakly primary submodules over non-commutative rings are proved. We also introduce the definitions of weakly primary compactly packed and maximal compactly packed modules. Then we study the relation between these modules and investigate the condition on a left R −module M that makes the concepts of primary compactly packed modules and weakly primary compactly packed modules equivalent. We also introduce the concept of weakly primary radical submodules and show that every Bezout module that satisfies the ascending chain condition on weakly primary radical submodules is weakly primary compactly packed module.

Item Type: Article
Uncontrolled Keywords: Primary submodule; Weakly primary submodule; primary compactly packed module; weakly primary compactly packed module; maximal compactly packed module; weakly primary radicalsubmodule
Subjects: Q Science > QA Mathematics
Depositing User: د. محمد العبد محمد حمودة
Date Deposited: 10 May 2018 07:09
Last Modified: 10 May 2018 08:08
URI: http://scholar.alaqsa.edu.ps/id/eprint/738

Actions (login required)

View Item View Item