Some Aspects of d -Units in d / BCK-Algebras

Abstract

We explore properties of the set of d-units of a $d$-algebra. A property of interest in the study of $d$-units in $d$-algebras is the weak associative property. It is noted that many other $d$-algebras, especially $\text{B}\text{C}\text{K}$-algebras, are in fact weakly associative. The existence of $d/\text{B}\text{C}\text{K}$-algebras which are not weakly associative is demonstrated. Moreover, the notions of a $d$-integral domain and a left-injectivity are discussed.