MULTIPLICATION MODULES THAT ARE FINITELY GENERATED
Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication mo...
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| Format: | Article |
| Language: | English |
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Shahrood University of Technology
2020-09-01
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| Series: | Journal of Algebraic Systems |
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| Online Access: | http://jas.shahroodut.ac.ir/article_1761_b43d2dbad078483b14ce4c8a0a2df8fc.pdf |
| _version_ | 1818616174474166272 |
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| author | Y. Tolooei |
| author_facet | Y. Tolooei |
| author_sort | Y. Tolooei |
| collection | DOAJ |
| description | Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a characterization of finitely generated multiplication modules. |
| first_indexed | 2024-12-16T16:45:36Z |
| format | Article |
| id | doaj.art-e088d02a25a44503a87ed4aefd982116 |
| institution | Directory Open Access Journal |
| issn | 2345-5128 2345-511X |
| language | English |
| last_indexed | 2024-12-16T16:45:36Z |
| publishDate | 2020-09-01 |
| publisher | Shahrood University of Technology |
| record_format | Article |
| series | Journal of Algebraic Systems |
| spelling | doaj.art-e088d02a25a44503a87ed4aefd9821162022-12-21T22:24:12ZengShahrood University of TechnologyJournal of Algebraic Systems2345-51282345-511X2020-09-01811510.22044/jas.2019.8699.14211761MULTIPLICATION MODULES THAT ARE FINITELY GENERATEDY. Tolooei0Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149-67346, Iran.Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)\leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a characterization of finitely generated multiplication modules.http://jas.shahroodut.ac.ir/article_1761_b43d2dbad078483b14ce4c8a0a2df8fc.pdfmultiplication modulenoetherian ringfaithful module |
| spellingShingle | Y. Tolooei MULTIPLICATION MODULES THAT ARE FINITELY GENERATED Journal of Algebraic Systems multiplication module noetherian ring faithful module |
| title | MULTIPLICATION MODULES THAT ARE FINITELY GENERATED |
| title_full | MULTIPLICATION MODULES THAT ARE FINITELY GENERATED |
| title_fullStr | MULTIPLICATION MODULES THAT ARE FINITELY GENERATED |
| title_full_unstemmed | MULTIPLICATION MODULES THAT ARE FINITELY GENERATED |
| title_short | MULTIPLICATION MODULES THAT ARE FINITELY GENERATED |
| title_sort | multiplication modules that are finitely generated |
| topic | multiplication module noetherian ring faithful module |
| url | http://jas.shahroodut.ac.ir/article_1761_b43d2dbad078483b14ce4c8a0a2df8fc.pdf |
| work_keys_str_mv | AT ytolooei multiplicationmodulesthatarefinitelygenerated |