Positive implicative equality algebras and equality algebras with some types

Document Type : Original Article

Authors

1 Hatef Higher Education Institute, Zahedan, Iran

2 School of Mathematics, Northwest University, Xi'an 710127, China

3 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

4 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

Abstract

The notion of a positive implicative equality algebras are defined, and related properties are studied. Characterizations of a positive implicative equality algebra is investigated. Conditions for an equality algebra to be positive implicative are provided. Equality algebra with some types is considered, and several properties are investigated. Using equality algebra with some types, we characterize a commutative equality algebra and a positive implicative algebra.
 

Keywords

References

[1] S.Z. Alavi, R.A. Borzooei, M. Aaly Kologani, Fuzzy filters in pseudo hoops, Journal of Intelligent
and Fuzzy Systems, 32(3) (2017), 1997–2007.
[2] M. Aaly Kologani, R.A. Borzooei, G.R. Rezaei, Y.B. Jun, Commutative equality algebras and
&-equality algebras, Annals of the University of Craiova - Mathematics and Computer Science
Series, 47(2) (2020), 331-345.
[3] M. Aaly Kologani, M. Mohseni Takallo, R.A. Borzooei, Y.B. Jun, Implicative equality algebras
and annihilators in equality algebras, Journal of Discrete Mathematical Sciences and
Cryptography, (2021), DOI: 10.1080/09720529.2021.1876293.
[4] R.A. Borzooei, M.A. Hashemi, Tense like equality algebras, Categories and General Algebraic
Structures with Applications, 13(1) (2020), 143–166.
[5] R.A. Borzooei, M. Zarean, O. Zahiri, Involutive equality algebras, Soft Computing, 22 (2018),
7505–7517.
[6] S. Jenei, Equality algebras, Proceeding of CINTI 2010 conference-11th IEEE International
Symposium on Computational Intelligence and Informatics, Budapest, Hungary, 2010.
[7] S. Jenei, Equality algebras, Studia Logic, 100 (2012), 1201–1209.
[8] M. Mohseni Takallo, M. Aaly Kologani, MBJ-neutrosophic filters of equality algebras, Journal
of Algebraic Hyperstructures and Logical Algebras, 1(2) (2020), 57–75.
[9] V. Novák, B. De Baets, EQ-algebras, Fuzzy Sets and Systems, 160(2) (2009), 2956–2978.
[10] A. Paad, M. Bakhshi, Hyper equality ideals: Basic properties, Journal of Algebraic Hyperstructures
and Logical Algebras, 1(2) (2020), 45–56.
[11] P.V. Ramana Murty, Semi-Brouwerian algebras, Journal of the Australian Mathematical Society,
18 (1974), 293–302.
[12] G.R. Rezaei, M. Aaly Kologani, R.A. Borzooei, M. Mohseni Takallo, Derivations of equality
algebras, Soft Computing, (2022), DOI:10.21203/rs.3.rs-1224210/v1.
[13] M. Zarean, R.A. Borzooei, O. Zahiri, On state equality algebras, Quasigroups and Related
Systems, 25 (2017), 307–326.
[14] F. Zebardast, R.A. Borzooei, M. Aaly Kologani, Results on equality algebras, Information
Sciences, 381 (2017), 270–282.
Journal of Algebraic Hyperstructures and Logical Algebras
Volume 3, Issue 2
May 2022
Pages 69-86

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