Fuzzy maximal, radical and primary ideals of a ring

Davender S. Malik, John N. Mordeson

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

We introduce the concepts of fuzzy maximal ideal, the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring. We show that a fuzzy left (right) ideal A of a ring R is a fuzzy maximal ideal if and only A(0) = 1 and A* = {x ε{lunate} R:A(x) = A(0)} is a maximal left (right) ideal of R. We also show that a fuzzy ideal A of a commutative ring R with unity is a fuzzy primary ideal of R if and only A(0) = 1, A is two-valued and A* is a primary ideal of R.

Original languageEnglish
Pages (from-to)237-250
Number of pages14
JournalInformation Sciences
Volume53
Issue number3
DOIs
StatePublished - 1991

Fingerprint

Fuzzy Ideal
Ring
Maximal Ideal
Commutative Ring

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Information Systems
  • Information Systems and Management
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Statistics and Probability

Cite this

Fuzzy maximal, radical and primary ideals of a ring. / Malik, Davender S.; Mordeson, John N.

In: Information Sciences, Vol. 53, No. 3, 1991, p. 237-250.

Research output: Contribution to journalArticle

Malik, Davender S. ; Mordeson, John N. / Fuzzy maximal, radical and primary ideals of a ring. In: Information Sciences. 1991 ; Vol. 53, No. 3. pp. 237-250.
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