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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Veröffentlicht in:Journal of University of Anbar for Pure Science 2018-06, Vol.11 (3), p.102-109
Hauptverfasser: K. Mohammad ali, Haibat, S. Mohammed, Akram, D. Sallman, Mohammad
Format: Artikel
Sprache:eng
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Zusammenfassung:"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:2706-6703
1991-8941
2706-6703
DOI:10.37652/juaps.2017.148087