1. bookVolume 30 (2022): Edizione 1 (February 2022)
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Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
access type Accesso libero

Prime preideals on bounded EQ-algebras

Pubblicato online: 12 Mar 2022
Volume & Edizione: Volume 30 (2022) - Edizione 1 (February 2022)
Pagine: 5 - 30
Ricevuto: 16 Apr 2021
Accettato: 29 Jun 2021
Dettagli della rivista
License
Formato
Rivista
eISSN
1844-0835
Prima pubblicazione
17 May 2013
Frequenza di pubblicazione
1 volta all'anno
Lingue
Inglese
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.

Keywords

MSC 2010

[1] R. A. Borzooei, N. Akhlaghinia, M. Aaly Kologhani, Preideals in EQ-algebras, submitted. Search in Google Scholar

[2] R. A. Borzooei, N. Akhlaghinia, M. Aaly Kologani, X. L. Xin, The category of EQ-algebras, Bulletin of the Section of Logic, 50(1) (2021), https://doi.org/10.18778/0138-0680.2021.01.10.18778/0138-0680.2021.01 Search in Google Scholar

[3] R. A. Borzooei, B. Ganji, States On EQ-algebras, Journal of Intelligent and Fuzzy Systems, 29 (2015), 209-221.10.3233/IFS-151588 Search in Google Scholar

[4] S. Burris, H. P. Sankappanavar, A course in universal algebra (Graduate Texts in Mathematics), Springer-Verlag, 78 (1981).10.1007/978-1-4613-8130-3 Search in Google Scholar

[5] M. El-Zekey, Representable good EQ-algebras, Soft Computing, 14(9) (2010), 1011–1023.10.1007/s00500-009-0491-4 Search in Google Scholar

[6] M. El-Zekey, V. Novák, R. Mesiar, On good EQ-algebras, Fuzzy Sets and Systems, 178 (2011), 1–23.10.1016/j.fss.2011.05.011 Search in Google Scholar

[7] R. Engelking, General Topology (revised and completed edition), Heldermann Verlag, Berlin, (1989). Search in Google Scholar

[8] B. Ganji Sa ar, Fuzzy n-fold obstinate and maximal (pre)filters of EQ-algebras, Journal of Algebraic Hyperstructuresand Logical Algebras, 2 (1), 83–98.10.52547/HATEF.JAHLA.2.1.6 Search in Google Scholar

[9] M. Gehrke, S. J. van Gool, V. Marra, Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality, Journal of Algebra, 417 (2014), 290–332.10.1016/j.jalgebra.2014.06.031 Search in Google Scholar

[10] L. C. Holdon, On ideals in Demorgan residuated lattices, Kybernetika, 54(3) (2018), 443–475.10.14736/kyb-2018-3-0443 Search in Google Scholar

[11] L. Z. Liu, X. Y. Zhang, Implicative and positive implivative prefilters of EQ-algebras, Journal of Intelligent and Fuzzy Systems, 26 (2014), 2087–2097.10.3233/IFS-130884 Search in Google Scholar

[12] N. Mohtashamnia, L. Torkzadeh, B. Davvaz, Boolean center of lattice ordered EQ-algebras with bottom element, Journal of Algebraic Structures and Their Applications, 5(1) (2018), 51–68.10.29252/asta.5.1.51 Search in Google Scholar

[13] J. R. Munkres, Topology, Dorling Kindersley, India, (2000). Search in Google Scholar

[14] V. Novák, B. De Baets, EQ-algebras, Fuzzy Sets and Systems, 160 (2009), 2956–2978.10.1016/j.fss.2009.04.010 Search in Google Scholar

[15] X. L. Xin, Y. C. Ma, Y. L. Fu, The existence of states on EQ-algebras, Mathematica Slovaca, 70(3) (2020), 527–546.10.1515/ms-2017-0369 Search in Google Scholar

[16] J. Yang, X. L. Xin, P. F. He, Uniform topology on EQ-algebras, Open Mathematics, 15 (2017), 354–364.10.1515/math-2017-0032 Search in Google Scholar

[17] J. Yang, X. L. Xin, P. F. He, On topological EQ-algebras, Iranian Journal of Fuzzy Systems, 15(6) (2018), 145–158. Search in Google Scholar

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