Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

The varieties of Bol-Moufang quasigroups defined by a single Reza Akhtar

Summary: The varieties of Bol-Moufang quasigroups defined by a single
Reza Akhtar
Ashley Arp
Michael Kaminski
Jasmine Van Exel
Davian Vernon
Cory Washington
November 8, 2010
Mathematics Subject Classification: 20N05
Keywords: quasigroup, Bol-Moufang identity, variety
A quasigroup identity is said to be of Bol-Moufang type if it involves three
variables, two of which occur once on each side and one of which appears twice
on both sides; 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 Bol-Moufang type
where the operation involved is , /, or \, determining all inclusions among these
and providing all necessary counterexamples. This work extends that of Phillips
and Vojtechovsk´y, who described the relationships among the 26 varieties ob-


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


Collections: Mathematics