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Groupoids with the identity (xy)y=yx
by
Lidija Goracinova Ilieva
University 'St. Kiril and Metodij', Macedonia
Coauthors: Smile Markovski, Ana Sokolova
Two constructions of free groupoids in the variety V defined by Stein's identity (xy)y=yx are given. The first one is obtained by a few identities, but the universe and the operation are defined by induction. Namely, for a nonempty set B, a chain of partial groupoids (Rn, *n), n >= 1, is constructed in such a way that u*2nv is defined for each u, v in Rn. Then (R, *) is a free groupoid in V with free base B, where R= \cup (Rn|n >= 1) and *= \cup (*n|n >= 1). The second construction is a direct one and it is based on a countable system of identities of special forms and a suitable subset of the absolutely free groupoid with free base B.
Date received: November 3, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafo-14.