On block commutative groupoids

Abstract

In this paper, we introduce the notion of a block commutativity in several groupoids, and show that the class of block commutative groupoids and the class of d/BCKalgebras are Smarandache disjoint. The block commutativity in linear/quadratic groupoids is investigated, and we prove that every group is a normal groupoid. Moreover, we discuss block n-commutative groupoids and block ranks.