Solid Varieties of Type (n)
by
Shelly L. Wismath
University of Lethbridge
Coauthors: K. Denecke, J. Koppitz

A solid variety is a variety in which every identity also holds as a hyperidentity. For type (2), Denecke and Wismath showed that there are a countably infinite number of solid varieties of semigroups, and Polák later characterized all the solid semigroup varieties. For other types, we know only a few examples of solid varieties. For instance, for any type \tau, the variety RA of rectangular algebras is solid, as are the trivial variety and the largest variety of the type. We describe two constructions which give countably infinite chains of solid varieties for any type (n), where there is one n-ary operation symbol.

Date received: December 31, 2000