Prime fuzzy ideals over noncommutative rings

  • Authors:
  • Gabriel Navarro;Oscar Cortadellas;F. J. Lobillo

  • Affiliations:
  • Department of Computer Sciences and AI, University of Granada, C/El Greco s/n, E-51002 Ceuta, Spain;Department of Algebra, Faculty of Sciences, University of Granada, Avda. Fuentenueva s/n, E-18071 Granada, Spain;Department of Algebra, ETSIIT, University of Granada, c/ Periodista Daniel Saucedo Aranda s/n, E-18071 Granada, Spain

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

In this paper we introduce prime fuzzy ideals over a noncommutative ring. This notion of primeness is equivalent to level cuts being crisp prime ideals. It also generalizes the one provided by Kumbhojkar and Bapat in 1993, which lacks this equivalence in a noncommutative setting. Semiprime fuzzy ideals over a noncommutative ring are also defined and characterized as intersection of primes. This allows us to introduce the fuzzy prime radical and contribute to establish the basis of a Fuzzy Noncommutative Ring Theory.