Atlas home || Conferences | Abstracts | about Atlas

Universal Algebra and Lattice Theory (Dedicated to the 70th birthday of B. Csakany)
July 22-26, 2002
University of Szeged
Szeged, Hungary

Organizers
Agnes Szendrei, Laszlo Szabo, Miklos Dorman

View Abstracts
Conference Homepage

Equational Bounds: Determining Finite Algebras in Finitely Generated Varieties.
by
George F. McNulty
University of South Carolina
Coauthors: Zoltán Székely (Gallaudet University)

With every variety V we associate a function \betaV on the positive integers so that \betaV(n) is the least positive integer k such that for every algebra B with exactly n elements

B in V
if and only if
every equation of length no more than k which is true in V is true in B.

The function \betaV is called the equational bound of V. By the equational bound \betaA of the algebra A we mean the equational bound of the variety generated by A.

Here we investigate the assymptotic behavior of equational bounds for finite algebras. It is clear that if A is finitely based, then \betaA is eventually dominated by a constant function. So our investigation must focus on nonfinitely based algebras. We show in many cases that the equational bound is eventually dominated by a linear function. On the other hand, we describe a general method for constructing finite algebras with equational bounds that eventually dominate every sublinear function.

Date received: June 28, 2002

Copyright © 2002 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 # caiv-35.