Quasivarieties of commutative binary modes
by
Anna Romanowska
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, 00-661 Warsaw, Poland
Coauthors: Katarzyna Matczak (Warsaw, Poland)

Commutative binary modes are idempotent and entropic (or medial) groupoids with commutative multiplication. Their varieties were fully described by J. Jezek and T. Kepka, and their structure by A. Romanowska and J. D. H. Smith. It is well known that each cancellative commutative binary mode embeds into a commutative quasigroup mode. In this talk we will give a full description of the lattice of quasivarieties of cancellative commutative binary modes, and show that it is isomorphic to the lattice of quasivarieties of commutative quasigroup modes. We will also show how the quasivarieties of cancellative commutative binary modes determine quasivarieties of such non-cancellative groupoids.

Date received: January 31, 2003