K-Normalizations of Varieties
by
Shelly Wismath
University of Lethbridge, Canada
Coauthors: Klaus Denecke (University of Potsdam)

A non-trivial identity s \approx t is normal when neither of the terms s and t is a variable. Using the definition of the depth of a term, this requires exactly that both s and t have depth >= 1. We generalize this definition to any integer k >= 1, by saying that a non-trivial identity s \approx t is k-normal when both s and t have depth >= k. A variety will be called k-normal when all its non-trivial identities are k-normal. Using results from the theory of Galois-connections and complete sublattices, we show that the collection of all k-normal varieties of a fixed type forms a complete sublattice of the lattice of all varieties of the type. We also generalize to the k-normal case the results of Graczy\'nska ([Gra]) and Melnik ([Mel]) describing normal varieties and the mapping taking any variety to the least normal variety containing it.

Date received: March 12, 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 # cagi-31.