A triple construction on $d$-algebras

In this note, we consider a triple construction $(\text{ad};\star ,\epsilon (0))$ 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 $(\text{ad};<)$ is a poset, which induces a $BCK$-algebra.