Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica (Feb 2022)

Prime preideals on bounded EQ-algebras

  • Akhlaghinia N.,
  • Borzooei R. A.,
  • Kologani M. Aaly

DOI
https://doi.org/10.2478/auom-2022-0001
Journal volume & issue
Vol. 30, no. 1
pp. 5 – 30

Abstract

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EQ-algebras were introduced by Novák in [14] as an algebraic structure of truth values for fuzzy type theory (FFT). In [1], Borzooei et. al. introduced the notion of preideal in bounded EQ-algebras. In this paper, we introduce various kinds of preideals on bounded EQ-algebras such as Λ-prime, ⊗-prime, ∩-prime, ∩-irreducible, maximal and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded EQ-algebra, any proper preideal is included in a Λ-prime preideal. In the following, we show that the set of all Λ-prime preideals in a bounded EQ-algebra is a T0 space and under some conditions, it is compact, connected, and Hausdor. Moreover, we show that the set of all maximal preideals of a prelinear involutive bounded EQ-algebra is an Uryshon (Hausdor) space and for a finite EQ-algebra, it is T3 and T4 space. Finally, we introduce a contravariant functor from the categories of bounded EQ-algebras to the category of topological spaces.

Keywords