Fuzzy maximal, radical and primary ideals of a ring

D. S. Malik, John N. Mordeson

Research output: Contribution to journalArticle

43 Scopus citations

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 (US)
Pages (from-to)237-250
Number of pages14
JournalInformation sciences
Volume53
Issue number3
DOIs
StatePublished - Feb 1991

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management
  • Artificial Intelligence

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