MULTIPLICATION MODULES THAT ARE FINITELY GENERATED
Publish place: Journal of Algebraic Systems، Vol: 8، Issue: 1
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JAS-8-1_001
تاریخ نمایه سازی: 5 شهریور 1399
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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Authors
Y. Tolooei
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, ۶۷۱۴۹-۶۷۳۴۶, Iran.