On block commutative groupoids

Document Type : Original Article


1 Department of Mathematics, Daejin University, Pochen 11159, Korea

2 Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.

3 Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea


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/BCK-algebras 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.