MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Document Type : Original Manuscript

Author

Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149-67346, Iran.

Abstract

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.

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References

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Journal of Algebraic Systems
Volume 8, Issue 1
September 2020
Pages 1-5

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