Vol. 76, No. 2, 1978

Recent Issues
Vol. 330: 1
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Uniform representations of congruence schemes

Joel David Berman and George Grätzer

Vol. 76 (1978), No. 2, 301–311

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
Received: 21 December 1976
Revised: 10 September 1977
Published: 1 June 1978
Joel David Berman
George Grätzer