Subdirectly Irreducible Nonidempotent Left Distributive Left Quasigroups

Abstract

Abstract Left distributive left quasigroups are binary algebras with unique left division satisfying the left distributive identity x(yz) ≈ (xy)(xz). In other words, binary algebras where all left translations are automorphisms. We provide a description and examples of nonidempotent subdirectly irreducible algebras in this class. Key Words: Group conjugationGroupoidLeft distributiveLeft quasigroupSubdirectly irreducible2000 Mathematics Subject Classification: 20N0208B20 ACKNOWLEDGMENTS While working on this article, the author was supported by the Eduard \v Cech Center for Algebra and Geometry. A partial support by the grant GA\v CR 201/05/0002 is also acknowledged. Notes Communicated by A. Yu. Olshanskii.