Spectrum of prime L-fuzzy h-ideals of a hemiring

  • Authors:

  • H. V. Kumbhojkar

  • Affiliations:

  • Department of Mathematics, Addis Ababa University, Addis Ababa, Ethiopia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

We redefine the concept of prime fuzzy h-ideals of a hemiring so that the fuzzy h-ideals are not necessarily 2-valued. We also introduce the concept of semiprime fuzzy h-ideals. A topological space, called the spectrum of prime fuzzy h-ideals of a commutative hemiring with unity, has been obtained. This topological space is compact and preserves isomorphisms between hemirings. The correspondence associating a hemiring with its spectrum of prime fuzzy h-ideals is shown to define a contravariant functor from the category of commutative hemirings with unity into the category of compact topological spaces. The spectrum of (crisp) prime h-ideals of the hemiring is a subspace which is dense in the spectrum of prime fuzzy h-ideals. Valuation lattices for all the fuzzy sets in the paper are assumed to be complete Heyting algebras.