Varieties of residuated lattices generated by positive universal classes.
by
Nikolaos Galatos
Vanderbilt University

In a discriminator variety, V, for every first order formula, \phi, there exists a set of equations that serves as an equational basis for the subvariety generated by the subdirectly irreducible members of V that satisfy \phi. Even though the variety of residuated lattices is not a discriminator variety, we establish a similar result for it under the assumption that \phi is a positive universal formula (a first order formula that is universally quantified and can be written without negation and implication). As a corollary we get simple equational bases for several subvarieties that are generated by natural classes of residuated lattices, and we prove that the join of a pair of certain finitelly based varieties (including all commutative ones) is also finitely based.

Date received: February 18, 2002