Fractionary fuzzy ideals and Dedekind domains
type: Item
instance of: scholarly article
title: Fractionary fuzzy ideals and Dedekind domains
zbMATH Open document ID: 0943.13003
DOI: 10.1016/S0165-0114(97)00012-2
author: Kyoung Hee Lee
author: John N. Mordeson
published in: Fuzzy Sets and Systems
publication date: 2000-03-12T00:00:00Z
review text: This paper continues the investigation of the previously introduced notions of fractionary fuzzy ideals (a special fuzzy \(R\)-submodule of the quotient field of an integral domain \(R\)) and fuzzy invertible fractionary fuzzy ideals. It is shown that a finite-valued fractionary fuzzy ideal of an integral domain \(R\) with invertible level ideals has a finite minimal generating set. Moreover the authors give three characterizations of a Dedekind domain in terms of factorization of fuzzy ideals as products of prime fuzzy ideals as well as in terms of invertibility of some special fractionary fuzzy ideals. Finally some results are given concerning the factorization of fractionary fuzzy ideals.
reviewed by: E. E. Kerre
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 1398907
zbMATH Keywords: fractionary fuzzy ideals
zbMATH Keywords: Dedekind domain
zbMATH Keywords: factorization of fuzzy ideals
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1398907