Congruence relations and multiplicity types of algebras

Abstract

Given two multiplicity types and '', the following two conditions are shown to be equivalent: (1) For every algebra A of multiplicity type there exists an algebra A f of multiplicity type f such that A and A' have exactly the same congruence relations. (2) For every k > 0, k + k+1 + ^ + Introduction* Given an algebra A = < U, /<(i e /)>, we let Con (A) be the lattice of congruence relations over A. By the multiplicity type of A we mean the sequence = ( 0 , lf , n ,