CLASSICAL 2-ABSORBING SECONDARY SUBMODULES
In this work, we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules. Let $R$ be a commutative ring with identity. We say that a non-zero submodule $N...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahrood University of Technology
2020-09-01
|
| Series: | Journal of Algebraic Systems |
| Subjects: | |
| Online Access: | http://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdf |
| id |
doaj-1b89e3634528440abd70e4e18900a550 |
|---|---|
| record_format |
Article |
| spelling |
doaj-1b89e3634528440abd70e4e18900a5502021-02-09T06:50:25ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2020-09-018171510.22044/jas.2019.7287.13591762CLASSICAL 2-ABSORBING SECONDARY SUBMODULESF. Farshadifar0Department of Mathematics, Farhangian University, Tehran, Iran.In this work, we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules. Let $R$ be a commutative ring with identity. We say that a non-zero submodule $N$ of an $R$-module $M$ is a \emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a, b \in R$, $K$ is a submodule of $M$ and $abN\subseteq K$, then $aN \subseteq K$ or $bN \subseteq K$ or $ab \in \sqrt{Ann_R(N)}$. This can be regarded as a dual notion of the 2-absorbing primary submodule.http://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdfsecondary module2-absorbing primary idealclassical 2-absorbing secondary module |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
F. Farshadifar |
| spellingShingle |
F. Farshadifar CLASSICAL 2-ABSORBING SECONDARY SUBMODULES Journal of Algebraic Systems secondary module 2-absorbing primary ideal classical 2-absorbing secondary module |
| author_facet |
F. Farshadifar |
| author_sort |
F. Farshadifar |
| title |
CLASSICAL 2-ABSORBING SECONDARY SUBMODULES |
| title_short |
CLASSICAL 2-ABSORBING SECONDARY SUBMODULES |
| title_full |
CLASSICAL 2-ABSORBING SECONDARY SUBMODULES |
| title_fullStr |
CLASSICAL 2-ABSORBING SECONDARY SUBMODULES |
| title_full_unstemmed |
CLASSICAL 2-ABSORBING SECONDARY SUBMODULES |
| title_sort |
classical 2-absorbing secondary submodules |
| publisher |
Shahrood University of Technology |
| series |
Journal of Algebraic Systems |
| issn |
2345-5128 2345-511X |
| publishDate |
2020-09-01 |
| description |
In this work, we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules. Let $R$ be a commutative ring with identity. We say that a non-zero submodule $N$ of an $R$-module $M$ is a \emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a, b \in R$, $K$ is a submodule of $M$ and $abN\subseteq K$, then $aN \subseteq K$ or $bN \subseteq K$ or $ab \in \sqrt{Ann_R(N)}$. This can be regarded as a dual notion of the 2-absorbing primary submodule. |
| topic |
secondary module 2-absorbing primary ideal classical 2-absorbing secondary module |
| url |
http://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdf |
| work_keys_str_mv |
AT ffarshadifar classical2absorbingsecondarysubmodules |
| _version_ |
1724277730432778240 |