Further Results on Derivations of Ranked Bigroupoids

Abstract

Several authors [1–4] have studied derivations in rings and near rings. Jun and Xin [5] applied the notion of derivation in ring and near-ring theory to -algebras, and as a result they introduced a new concept, called a (regular) derivation, in -algebras. Zhan and Liu [6] studied -derivations in -algebras. Alshehri [7] applied the notion of derivations to incline algebras. Alshehri et al. [8] introduced the notion of ranked bigroupoids and discussed -self-(co)derivations. In this paper, we investigate further properties on -self-(co)derivations and provide conditions for an -self-(co)derivation to be regular. We introduce the notion of ranked -subsystems and investigate related properties.