Spectrum of prime fuzzy ideals
type: Item
instance of: scholarly article
title: Spectrum of prime fuzzy ideals
zbMATH Open document ID: 0832.54004
DOI: 10.1016/0165-0114(94)90077-9
author: H. V. Kumbhojkar
published in: Fuzzy Sets and Systems
publication date: 1996-03-05T00:00:00Z
review text: An attempt has been made to introduce an appropriate topology on the set of prime fuzzy ideals. Instead of appealing to other definitions of prime fuzzy ideals, as in literature, the author has taken his own definition introduced earlier; such prime fuzzy ideals in a commutative ring \(R\) with identity are denoted by \(F \text{spec} (R)\); the author has studied \(F \text{spec} (R)\) with an appropriate topology and has studied many interesting properties. Situations under which fuzzy spectra of different rings are homeomorphic are discussed; in particular, \(F \text{spec} (R)\) is proved to be homeomorphic to \(F \text{spec} (R/F \text{rad} (R))\), where \(F \text{rad} (R)\) is the fuzzy prime radical of \(R\). The correspondence associating a ring \(R\) to the topological space \(F \text{spec} (R)\) is shown to define a contravariant functor from the category of rings with unity, into the category of compact topological spaces.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 788364
zbMATH Keywords: prime fuzzy ideals
zbMATH Keywords: contravariant functor
reviewed by: Sobhakar Ganguly
MaRDI profile type: Publication
full work available at URL: 0165-0114(94)90077-9
OpenAlex ID: W2017802727
cites work: Q5563439
cites work: Q3956998
cites work: L-fuzzy sets
cites work: Not-so-fuzzy fuzzy ideals
cites work: Correspondence theorem for fuzzy ideals
cites work: On prime and primary fuzzy ideals and their radicals
cites work: On semiprime fuzzy ideals
cites work: Fuzzy invariant subgroups and fuzzy ideals
cites work: Fuzzy ideals of Artinian rings
cites work: Fuzzy prime ideals of a ring
cites work: Fuzzy maximal, radical, and primary ideals of a ring
cites work: Fuzzy primary representations of fuzzy ideals
cites work: On fuzzy ideals of a ring. I
cites work: Q4039952
cites work: Fuzzy prime ideals of rings
cites work: Fuzzy prime ideals and fuzzy radical ideals
cites work: Prime L-fuzzy ideals and primary L-fuzzy ideals
cites work: A characterization of \(L\)-fuzzy prime ideals
description: scientific article; zbMATH DE number 788364