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AAA60: Workshop on General Algebra (60. Arbeitstagung Allgemeine Algebra)
June 22-25, 2000
Dresden University of Technology
Dresden, Germany

Organizers
Reinhard Pöschel, Manfred Droste, Bernhard Ganter

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On the groupoid identity x(xy)=y
by
Ana Sokolova
Institute of Informatics, Faculty of Sciences, Skopje, Macedonia
Coauthors: Smile Markovski (II, Faculty of Sciences, Skopje, Macedonia), Lidija Gorachinova (PF, Shtip, Macedonia)

The groupoid identity x(xy)=y appears in many classes of groupoids like Steiner loops (or totally symmetric quasigroups) and in connection with groupoids orthogonal to quasigroups. We consider several varieties of groupoids with the identity x(xy)=y such as: V(x(xy)=y), V(x(xy)=y, (yx)x = x), V(x(xy)=y, (yx)x = yx), V(x(xy)=y, (yx)x=xy). Cannonical construction of the free objects in each of these varieties is presented. For some of them in evidence of the presented constructions structural properties of the free objects and of the finite groupoids are obtained.

Date received: May 22, 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 # caee-59.