NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS

author

  • A. Yousefian Darani Department of Mathematics and Applications, University of Mohaghegh Ardabili, P.O.Box 5619911367, Ardabil, Iran.
Abstract:

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.

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Journal title

volume 3  issue 2

pages  201- 210

publication date 2015-01-01

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