Prime preideals on bounded EQ-algebras

• Published in: Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Vol. 30; no. 1; pp. 5 - 30
• Main Authors: Akhlaghinia, N., Borzooei, R. A., Kologani, M. Aaly
• Format: Journal Article
• Language: English
• Published: Sciendo 01.02.2022
• Subjects: algebras; eq-algebras; ideals; maximal preideals; preideals; Primary 06E15, 06F99; prime preideals; Secondary 06B10, 54F65; topology
• ISSN: 1844-0835; 1844-0835
• DOI: 10.2478/auom-2022-0001

-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 -algebras. In this paper, we introduce various kinds of preideals on bounded -algebras such as Λ- , ⊗- , ∩- , ∩- , and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded -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 -algebra is a 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 -algebra is an Uryshon (Hausdor) space and for a finite -algebra, it is and space. Finally, we introduce a contravariant functor from the categories of bounded algebras to the category of topological spaces.