Primary decompositions of fuzzy submodules
type: Item
instance of: scholarly article
zbMATH Open document ID: 0978.13001
author: Babington Makamba
author: V. Murali
publication date: 2002-02-12T00:00:00Z
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1587673
zbMATH Keywords: primary fuzzy submodules
zbMATH Keywords: primary decomposition
zbMATH Keywords: minimal primes
MaRDI profile type: Publication
title: Primary decompositions of fuzzy submodules
published in: The Journal of Fuzzy Mathematics
review text: Let \(R\) be a commutative ring with identity and let \(M\) be a unitary module over \(R\). In this paper, the authors consider the decomposition of a fuzzy submodule of \(M\) into an intersection of primary fuzzy submodules of \(M\). The authors prove two uniqueness theorems concerning such a decomposition. They show that such a decomposition exists when \(M\) is Noetherian. They also consider the notions of reduced or irredundant primary decompositions, irreducible decompositions, isolated and embedded prime ideals. The authors provide some pertinent counterexamples. They apply their decomposition theory to characterize an infinite intersection of fuzzy submodules of a Noetherian module as a zero fuzzy submodule. The results are analogues of the Krull intersection theorem.
reviewed by: John N. Mordeson
description: scientific article