2-Maximal Submodules and Related Concepts

"Throughout this paper R represents commutative ring with identity and M is unitary left R-module", the purpose of this paper is to study new concept (up to our knowledge) , named 2-maximal submodule which is a generalization of maximal submodule , "where a submodule N of an R-module...

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Bibliographic Details
Published in:	مجلة جامعة الانبار للعلوم الصرفة Vol. 11; no. 3; pp. 102 - 109
Main Authors:	Haibat K. Mohammad ali, Akram S. Mohammed, Mohammad D. Sallman
Format:	Journal Article
Language:	English
Published:	University of Anbar 01-06-2018
Online Access:	Get full text
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Summary:	"Throughout this paper R represents commutative ring with identity and M is unitary left R-module", the purpose of this paper is to study new concept (up to our knowledge) , named 2-maximal submodule which is a generalization of maximal submodule , "where a submodule N of an R-module M is called 2-maximal" submodul of M if and only if M/N is 2-regular R-module . Many characterizations and properties of 2-maximal submodules are given . Moreover we studied the behavior of 2-maximal submodule in some classes of module . Finally we give the sufficient condition 2-maximal submodules to be semi-maximal weak-maximal submodules are introduced .
ISSN:	1991-8941 2706-6703
DOI:	10.37652/juaps.2017.148087