A triple construction on $d$-algebras

Abstract

In this note, we consider a triple construction $(\ad;\star,ε(0))$ 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.

presented at the 11th National Mathematics Conference of Payam Noor University, October of 2024