<abstract xmlns="http://www.w3.org/1999/xhtml">

<italic>EQ</italic>-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 <italic>EQ</italic>-algebras. In this paper, we introduce various kinds of preideals on bounded <italic>EQ</italic>-algebras such as Λ-<italic>prime</italic>, ⊗-<italic>prime</italic>, ∩-<italic>prime</italic>, ∩-<italic>irreducible</italic>, <italic>maximal</italic> and then we investigate some properties and the relations among them. Specially, we prove that in a prelinear and involutive bounded <italic>EQ</italic>-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 <italic>EQ</italic>-algebra is a <italic>T</italic>0 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 <italic>EQ</italic>-algebra is an Uryshon (Hausdor) space and for a finite <italic>EQ</italic>-algebra, it is <italic>T</italic>3 and <italic>T</italic>4 space. Finally, we introduce a contravariant functor from the categories of bounded <italic>EQ-</italic>algebras to the category of topological spaces.
</abstract>

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.

Prime preideals on bounded <italic>EQ</italic>-algebras

Department of Mathematics, Faculty of Mathematical Sciences

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":{"italic":"EQ","content":["Prime preideals on bounded","-algebras"]}}

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...

Prime preideals on bounded EQ-algebras

Published Online: Mar 12, 2022

Page range: 5 - 30

Received: Apr 16, 2021

Accepted: Jun 29, 2021

DOI: https://doi.org/10.2478/auom-2022-0001

Keywords
-algebras, ideals, prime preideals, preideals, maximal preideals, topology

© 2022 N. Akhlaghinia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Prime preideals on bounded EQ-algebras

Published Online: Mar 12, 2022

Page range: 5 - 30

Received: Apr 16, 2021

Accepted: Jun 29, 2021

DOI: https://doi.org/10.2478/auom-2022-0001

Keywords-algebras, ideals, prime preideals, preideals, maximal preideals, topology

© 2022 N. Akhlaghinia et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
-algebras, ideals, prime preideals, preideals, maximal preideals, topology