Rectangular loops and rectangular quasigroups
arXiv:math/0409074
Abstract
We solve two problems posed by Krapež 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.
5 pages, AMS-LaTeX; v.2: minor corrections of proofs; v.3: added section discussing use of automated reasoning, other minor changes at request of referees