Canonical biassociative groupoids
Biljana Janeva, Snežana Ilić, Vesna Celakoska-Jordanova · Publications de l Institut Mathematique · 2007
In the paper Free biassociative groupoids, the variety of biassociative groupoids (i.e., groupoids satisfying the condition: every subgroupoid generated by at most two elements is a subsemigroup) is considered and free objects are constructed using a chain of partial biassociative groupoids that satisfy certain properties. The obtained free objects in this variety are not canonical. By a canonical groupoid in a variety V of groupoids we mean a free groupoid (R, ?) in V with a free basis B such that the carrier R is a subset of the absolutely free groupoid (TB, ?) with the free basis B and (tu ? R ? t, u ? R & t?u = tu). In the present paper, a canonical description of free objects in the variety of biassociative groupoids is obtained.