Subdirectly Irreducible Nonidempotent Left Distributive Left Quasigroups

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 conjugation
• Groupoid
• Left distributive
• Left quasigroup
• Subdirectly irreducible

2000 Mathematics Subject Classification:

• 20N02
• 08B20

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.