Summary: The varieties of Bol­Moufang quasigroups defined by a single
operation
Reza Akhtar
Ashley Arp
Michael Kaminski
Jasmine Van Exel
Davian Vernon
Cory Washington
November 8, 2010
Mathematics Subject Classification: 20N05
Keywords: quasigroup, Bol­Moufang identity, variety
Abstract
A quasigroup identity is said to be of Bol­Moufang type if it involves three
variables, two of which occur once on each side and one of which appears twice;
moreover, the order in which the variables appear is the same on both sides,
and there is only one binary operation in the identity. Answering a question
of Drap’al, we classify all varieties of quasigroups of Bol­Moufang type where
the operation involved is #, /, or \, determining all inclusions among these and
providing all necessary counterexamples. This work extends that of Phillips and
Vojt–echovsk’y, who described the relationships among the 26 varieties obtained

Source: Akhtar, Reza - Department of Mathematics and Statistics, Miami University (Ohio)

Collections: Mathematics