Transitivity of implicative aBE algebras

TL;DR

This paper proves that all implicative aBE algebras inherently satisfy transitivity, making them equivalent to Tarski algebras and commutative BCK algebras, thus establishing a key algebraic property.

Contribution

It demonstrates that implicative aBE algebras always satisfy transitivity, linking them to well-known algebraic structures and expanding their theoretical understanding.

Findings

Implication of transitivity in implicative aBE algebras.

Equivalence to Tarski and commutative BCK algebras.

Foundation for further algebraic property analysis.

Abstract

We prove that every implicative aBE algebra satisfies the transitivity property. This means that every implicative aBE algebra is a Tarski algebra, and thus is also a commutative BCK algebra.