Uniform representations of congruence schemes

Joel David Berman and George Grätzer

Vol. 76 (1978), No. 2, 301–311

DOI: 10.2140/pjm.1978.76.301

Abstract

A congruence scheme Σ is a finite sequence of polynomials. A nontrivial equational class K is a representation of Σ iff the principal congruences in K can be described in a natural fashion by Σ. In this paper it is shown that a necessary and sufficient condition for a congruence scheme Σ whose polynomials do not contain constants to have a representation is that each polynomial in the sequence be at least binary.

Mathematical Subject Classification

Primary: 08A25, 08A25

Milestones

Received: 21 December 1976

Revised: 10 September 1977

Published: 1 June 1978