General Implicativity in Groupoids

Abstract

There are several equivalent axioms, which can be used to characterize the positive implicativity in B C K -algebras. In this paper, we investigate interrelationships among such axioms in a more general setting of groupoids, and several aspects regarding their differences in the theory of groupoids.

Keywords

• groupoid
• <i>d</i>-algebra
• <i>BCK</i>-algebra
• (positive, central, meet, quasi) implicativity
• leftoid
• rightoid
• (selective, medial) groupoid