Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 2, pp. 327-336 (2009)
On torsion free distributive modules
Naser ZamaniFaculty of Science, University of Mohaghegh Ardabili, P.O.box 179, Ardabil, Iran; e-mail: firstname.lastname@example.org
Abstract: Let $R$ be a commutative ring with identity and let $M$ be a torsion free $R$-module. Several characterizations of distributive modules are investigated. Indeed, among other equivalent conditions, we prove that $M$ is distributive if and only if any primal submodule of $M$ is irreducible, and, if and only if each submodule of $M$ can be represented as an intersection of irreducible isolated components.
Keywords: distributive modules, associated primes
Classification (MSC2000): 13C99
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Electronic version published on: 28 Aug 2009. This page was last modified: 28 Jan 2013.