Rectangular Quasigroups and Rectangular Loops

摘要

We solve two problems posed by Krapez by finding a basis of seven independent axioms for the variety of rectangular loops. Six of these axioms form a basis for the variety of rectangular quasigroups. The proofs of the lemmas showing that the six axioms are sufficient are based on proofs generated by the automated reasoning program OTTER, while most of the models verifying the independence of the axioms were generated by the finite model builder MACE4.