Free Biassociative Groupoids

Snežana Ilić, Biljana Janeva, Naum Celakoski

The subject of this paper is the study of the variety of groupoids that have the following property: each subgroupoid generated by two elements is a subsemigroup. A construction of free objects in this variety is given. Free objects in the variety of idempotent and commutative groupoids with the mentioned property are also constructed.