Term-valuated Equational Theory
by
Klaus Denecke
University of Potsdam, Germany

A term valuation is a special homomorphism from the term algebra into another algebra of the same type on which a partial order relation is defined. Examples are the operation symbol count of a term, the variable count, the minimum depth and the maximum depth of a term. For a given equational theory, for a given valuation and for a given natural number k we ask for all equations from the equational theory such that both sides are terms of a value greater or equal to k. The model classes of such sets of equations, called k-normalizations of the given equational theories, form complete sublattices of the lattice of all varieties of the given type. An important problem is to find a generating set of the set of all identities of the k-normalization using the generating system of the given variety.

Date received: December 31, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-31.