NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS | ||
| Journal of Algebraic Systems | ||
| مقاله 8، دوره 3، شماره 2، فروردین 2016، صفحه 201-210 اصل مقاله (127.13 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2015.618 | ||
| نویسنده | ||
| A. Yousefian Darani* | ||
| Department of Mathematics and Applications, University of Mohaghegh Ardabili, P.O.Box 5619911367, Ardabil, Iran. | ||
| چکیده | ||
| In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modules are also true for Nonnil-Noetherian modules. | ||
| کلیدواژهها | ||
| Noetherian rings؛ Noetherian modules, Finitely generated submodules, Divided submodules, Phi-modules | ||
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