Not-so-fuzzy fuzzy ideals
type: Item
instance of: scholarly article
title: Not-so-fuzzy fuzzy ideals
zbMATH Open document ID: 0709.16001
DOI: 10.1016/0165-0114(90)90046-9
author: H. V. Kumbhojkar
author: M. S. Bapat
published in: Fuzzy Sets and Systems
publication date: 1990-01-01T00:00:00Z
review text: The authors look for algebraic structures which do not admit proper fuzzy substructures. The main answer is the following: Theorem. If a ring R is Boolean, Artinian or a principal ideal domain, then in R any proper prime fuzzy ideal P has supp P\(=\{0\}\). As a generalization they get a characterization of rings with finite chains of ideals. Similar results were recently presented by \textit{D. S. Malik}, \textit{J. N. Mordeson} [Fuzzy Sets Syst. 37, 93-98 (1990; Zbl 0704.16002)] and \textit{D. S. Malik} [ibid. 37, 111-115 (1990; Zbl 0704.16017)].
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16P20
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4165093
zbMATH Keywords: artinian ring
zbMATH Keywords: Boolean ring
zbMATH Keywords: fuzzy substructures
zbMATH Keywords: principal ideal domain
zbMATH Keywords: prime fuzzy ideal
zbMATH Keywords: rings with finite chains of ideals
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0165-0114(90)90046-9
OpenAlex ID: W1999162158
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description: scientific article; zbMATH DE number 4165093