MULTIPLICATION MODULES THAT ARE FINITELY GENERATED | ||
| Journal of Algebraic Systems | ||
| مقاله 1، دوره 8، شماره 1، آذر 2020، صفحه 1-5 اصل مقاله (114.84 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8699.1421 | ||
| نویسنده | ||
| Y. Tolooei* | ||
| Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149-67346, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Multiplication module؛ Noetherian Ring؛ faithful module | ||
| مراجع | ||
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