A triple construction on $d$-algebras

TL;DR

This paper introduces a triple construction on d-algebras, explores its properties, and demonstrates how it induces a poset and BCK-algebra from a d-transitive d-algebra.

Contribution

It presents a novel triple construction on d-algebras and shows its application in deriving poset and BCK-algebra structures.

Findings

The triple construction $( ext{ad};igstar, ext{ε}(0))$ has specific algebraic properties.

Applying the construction to a d-transitive d-algebra yields a poset.

The induced poset leads to a BCK-algebra.

Abstract

In this note, we consider a triple construction $(\ad;\star,\epsilon(0))$ on a $d$-algebra $(A;\ast,0)$ and investigate some of their properties. Applying this construction to a $d$-transitive $d$-algebra, we show that $(\ad; <)$ is a poset, which induces a $BCK$-algebra.