Pseudo Equality Algebras -- Revision

TL;DR

This paper explores the structure of pseudo equality algebras, establishing their relation to equality algebras and pseudo BCK-algebras, and characterizes their algebraic properties and congruences.

Contribution

It introduces a new type of pseudo equality algebra that better reflects its connection to pseudo BCK-algebras and analyzes their algebraic properties.

Findings

Every pseudo equality algebra is an equality algebra.

The variety of pseudo equality algebras is subtractive, congruence distributive, and congruence permutable.

Congruences are described via normal closed deductive systems.

Abstract

Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and K\'or\'odi to pseudo equality algebras which are aimed to find a connection with pseudo BCK-algebras with meet. We show that every pseudo equality algebra is an equality algebra. Therefore, we define a new type of pseudo equality algebras which more precisely reflects the relation to pseudo BCK-algebras with meet in the sense of Kabzi\'nski and Wro\'nski. We describe congruences via normal closed deductive systems, and we show that the variety of pseudo equality algebras is subtractive, congruence distributive and congruence permutable.