Congruence relations and multiplicity types of algebras

Bjarni Jónsson and Thomas Paul Whaley

Vol. 50 (1974), No. 2, 505–520

DOI: 10.2140/pjm.1974.50.505

Abstract

Given two multiplicity types μ and μ′, the following two conditions are shown to be equivalent: (1) For every algebra A of multiplicity type μ there exists an algebra A′ of multiplicity type μ′ such that A and A′ have exactly the same congruence relations. (2) For every k > 0,μ_k + μ_k+1 + ⋯ ≦ μ_k′+ μ_k+1′ + ⋯ .

Mathematical Subject Classification

Primary: 08A25

Milestones

Received: 6 October 1972

Published: 1 February 1974