Quasi pseudo equality algebras (BCK-algebras)

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Sistan and Baluchestan, Zahedan, Iran

2 Hatef Higher Education Institute, Zahedan, Iran

3 Department of Mathematics, Payam e Noor University, Tehran, Iran

4 Soft Computing and Artificial Intelligence Center, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

10.48308/cgasa.2026.243039.1595

Abstract

In this paper, by using the notions of ``quasi" and ``pseudo" in logical algebras,  we introduce two generalizations of equality algebras.  A commutative generalization of  equality algebras, is called quasi-equality algebras and a non-commutative generalization of quasi-equality algebras is called quasi-pseudo equality algebras. Then we investigate some of their properties. In addition, according to \cite{2} and knowing the relation between equality algebras and BCK(C)-meet-semilattices,  we generalize the concepts of BCK-algebras to quasi-BCK-algebras and pseudo BCK-algebras to quasi-pseudo BCK-algebras, too. The related properties and the relation between different kinds of quasi-(pseudo) BCK-algebras are investigated. Moreover, we investigate   the category of quasi-(pseudo) equality algebras and quasi-(pseudo) BCK-algebras and we show that they  are equivalent.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 28 June 2026

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