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Axiomatization of quasigroups

Jonathan D.H. Smith (2006)

Discussiones Mathematicae - General Algebra and Applications

Quasigroups were originally described combinatorially, in terms of existence and uniqueness conditions on the solutions to certain equations. Evans introduced a universal-algebraic characterization, as algebras with three binary operations satisfying four identities. Now, quasigroups are redefined as heterogeneous algebras, satisfying just two conditions respectively known as hypercommutativity and hypercancellativity.

Axioms for trimedial quasigroups

Michael K. Kinyon, Jon D. Phillips (2004)

Commentationes Mathematicae Universitatis Carolinae

We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial.

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