Fuzzy ideals and fuzzy semiprime ideals: Some ring theoretic analogues
type: Item
instance of: scholarly article
title: Fuzzy ideals and fuzzy semiprime ideals: Some ring theoretic analogues
zbMATH Open document ID: 0799.16003
DOI: 10.1016/0020-0255(92)90086-N
author: Rajesh Kumar
published in: Information Sciences
publication date: 1992-10-04T00:00:00Z
review text: The author contributes to the straightforward fuzzification of the concept ideal in a ring. Some interesting analogues of the classical results are obtained: -- The fuzzy nil radical of the \(n\)th power of a fuzzy prime ideal equals itself. -- Under rather general supplementary conditions it is shown that a fuzzy ideal of a ring is fuzzy primary if its fuzzy nil radical is a fuzzy maximal ideal of this ring. -- There exists a one-to-one correspondence between the set of all \(f\)-invariant fuzzy semiprime ideals of a ring \(R\) and the set of all fuzzy semiprime ideals of a ring \(R'\) where \(f\) denotes a surjective homomorphism between \(R\) and \(R'\).
Mathematics Subject Classification ID: 16D25
Mathematics Subject Classification ID: 16D10
Mathematics Subject Classification ID: 16N40
zbMATH DE Number: 68663
zbMATH Keywords: fuzzification
zbMATH Keywords: fuzzy nil radical
zbMATH Keywords: fuzzy prime ideal
zbMATH Keywords: fuzzy maximal ideal
zbMATH Keywords: fuzzy semiprime ideals
reviewed by: E. E. Kerre
MaRDI profile type: Publication
cites work: Fuzzy subgroups: some characterizations
cites work: Fuzzy groups: Some group theoretic analogs. II
cites work: On fuzzy rings
cites work: Fuzzy ideals and fuzzy prime ideals of a ring
cites work: Fuzzy vector spaces and fuzzy topological vector spaces
cites work: Certain fuzzy ideals of rings redefined
cites work: Fuzzy nil radicals and fuzzy primary ideals
cites work: Fuzzy semiprime ideals in semigroups
cites work: Fuzzy invariant subgroups and fuzzy ideals
cites work: Operations on fuzzy ideals
cites work: Fuzzy groups: Some group-theoretic analogues
cites work: On fuzzy ideals of a ring. I
cites work: Fuzzy groups
cites work: Fuzzy prime ideals of rings
cites work: Prime L-fuzzy ideals and primary L-fuzzy ideals
cites work: Fuzzy sets
full work available at URL: 0020-0255(92)90086-n
OpenAlex ID: W2089665300
description: scientific article; zbMATH DE number 68663