Short equational bases for MV-Algebras, commutative BCK-Algebras and {\L}BCK-algebras

TL;DR

This paper establishes minimal equational bases for MV-algebras, commutative BCK-algebras, and { extlangle}BCK-algebras, simplifying their algebraic characterizations.

Contribution

It provides concise 2-based axiomatizations for these algebraic structures, enhancing understanding and potential applications.

Findings

MV-algebras are 2-based varieties

Elegant 2-bases for commutative BCK-algebras

Simplified axiomatizations for { extlangle}BCK-algebras

Abstract

We show that the variety of MV-algebras is $2$-based and we offer elegant $2$-bases for the varieties of commutative BCK-algebras and {\L}BCK-algebras.