Congruence relations and multiplicity types of algebras
Bjàrni Jónsson, Thomas P. Whaley · Pacific Journal of Mathematics · 1974
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 f of multiplicity type μ f such that A and A' have exactly the same congruence relations.(2) For every k > 0, μ k + μ k+1 + ^ μί + Introduction* Given an algebra A = , we let Con (A) be the lattice of congruence relations over A. By the multiplicity type of A we mean the sequence μ = (μ 0 , μ lf, μ n , •> where μ n is the number of indices i for which the rank of /< is n.The purpose of this paper is to prove the following result: