On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings
Let G be an abelian group with identity ee. Let R be a G-graded commutative ring with identity 1, and MM be a graded R-module. In this paper, we introduce the concept of graded Jgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some r...
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2021
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oai:doaj.org-article:f716161f91554deba802458adea547fe2021-12-05T14:10:45ZOn graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings2391-466110.1515/dema-2021-0015https://doaj.org/article/f716161f91554deba802458adea547fe2021-06-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0015https://doaj.org/toc/2391-4661Let G be an abelian group with identity ee. Let R be a G-graded commutative ring with identity 1, and MM be a graded R-module. In this paper, we introduce the concept of graded Jgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerning of these classes of graded submodules. A proper graded submodule CC of MM is called a graded Jgr{J}_{gr}-classical 2-absorbing submodule of MM, if whenever rg,sh,ti∈h(R){r}_{g},{s}_{h},{t}_{i}\in h\left(R) and xj∈h(M){x}_{j}\in h\left(M) with rgshtixj∈C{r}_{g}{s}_{h}{t}_{i}{x}_{j}\in C, then either rgshxj∈C+Jgr(M){r}_{g}{s}_{h}{x}_{j}\in C+{J}_{gr}\left(M) or rgtixj∈C+Jgr(M){r}_{g}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M) or shtixj∈C+Jgr(M),{s}_{h}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M), where Jgr(M){J}_{gr}\left(M) is the graded Jacobson radical.Al-Zoubi KhaldounAlghueiri ShathaDe Gruyterarticlegraded jgr -classical 2-absorbing submodulegraded classical 2-absorbing submodulegraded 2-absorbing submodule13a0216w50MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 162-167 (2021) |
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graded jgr -classical 2-absorbing submodule graded classical 2-absorbing submodule graded 2-absorbing submodule 13a02 16w50 Mathematics QA1-939 |
| spellingShingle |
graded jgr -classical 2-absorbing submodule graded classical 2-absorbing submodule graded 2-absorbing submodule 13a02 16w50 Mathematics QA1-939 Al-Zoubi Khaldoun Alghueiri Shatha On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| description |
Let G be an abelian group with identity ee. Let R be a G-graded commutative ring with identity 1, and MM be a graded R-module. In this paper, we introduce the concept of graded Jgr{J}_{gr}-classical 2-absorbing submodule as a generalization of a graded classical 2-absorbing submodule. We give some results concerning of these classes of graded submodules. A proper graded submodule CC of MM is called a graded Jgr{J}_{gr}-classical 2-absorbing submodule of MM, if whenever rg,sh,ti∈h(R){r}_{g},{s}_{h},{t}_{i}\in h\left(R) and xj∈h(M){x}_{j}\in h\left(M) with rgshtixj∈C{r}_{g}{s}_{h}{t}_{i}{x}_{j}\in C, then either rgshxj∈C+Jgr(M){r}_{g}{s}_{h}{x}_{j}\in C+{J}_{gr}\left(M) or rgtixj∈C+Jgr(M){r}_{g}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M) or shtixj∈C+Jgr(M),{s}_{h}{t}_{i}{x}_{j}\in C+{J}_{gr}\left(M), where Jgr(M){J}_{gr}\left(M) is the graded Jacobson radical. |
| format |
article |
| author |
Al-Zoubi Khaldoun Alghueiri Shatha |
| author_facet |
Al-Zoubi Khaldoun Alghueiri Shatha |
| author_sort |
Al-Zoubi Khaldoun |
| title |
On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| title_short |
On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| title_full |
On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| title_fullStr |
On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| title_full_unstemmed |
On graded Jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| title_sort |
on graded jgr-classical 2-absorbing submodules of graded modules over graded commutative rings |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/f716161f91554deba802458adea547fe |
| work_keys_str_mv |
AT alzoubikhaldoun ongradedjgrclassical2absorbingsubmodulesofgradedmodulesovergradedcommutativerings AT alghueirishatha ongradedjgrclassical2absorbingsubmodulesofgradedmodulesovergradedcommutativerings |
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