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Universal Algebra and Lattice Theory (Dedicated to the 70th birthday of B. Csakany)
July 22-26, 2002
University of Szeged
Szeged, Hungary

Organizers
Agnes Szendrei, Laszlo Szabo, Miklos Dorman

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Relational equations, relational varieties and minimal relational clones
by
Reinhard Pöschel
Technische Universität Dresden

The talk presents results investigated mainly by J.-U. GRABOWSKI. Relational clones are closed w.r.t. primitive positive formulas. In analogy to universal algebras (where term operations are given by the clone of operations of an algebra), this gives rise to the notion of "term relation" as well as "relational equation".

In the talk we discuss equationally defined classes of relational systems and relational varieties (= classes closed under retracts and products). The property of having a minimal relational clone can be expressed by relational equations. An equational bases can be given explicitly for all but one classes of relational systems which correspond to the Rosenberg-classes of algebras with maximal clones.

Date received: June 11, 2002

Copyright © 2002 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 # caiv-22.