NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS

Document Type : Original Manuscript

Author

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.

Keywords

Journal of Algebraic Systems
Volume 3, Issue 2
January 2016
Pages 201-210

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