TY - JOUR ID - 1761 TI - MULTIPLICATION MODULES THAT ARE FINITELY GENERATED JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Tolooei, Y. AD - Department of Mathematics, Faculty of Science, Razi University, Kermanshah, 67149-67346, Iran. Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 1 EP - 5 KW - Multiplication module KW - Noetherian Ring KW - faithful module DO - 10.22044/jas.2019.8699.1421 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_1761.html L1 - https://jas.shahroodut.ac.ir/article_1761_b43d2dbad078483b14ce4c8a0a2df8fc.pdf ER -