Tolerances and congruences on tree algebras

Complemented congruences on Ockham algebras

An Ockham algebra L = (L,∧,∨, f, 0, 1) that satisfies the identity f2n+m = fm, n ∈ N and m ∈ N0, is called a Kn,m-algebra. Generalizing some results obtained in [2], J. Varlet and T. Blyth, in [3, Chapter 8], study congruences on K1,1-algebras. In particular, they describe the complement (when it exists) of a principal congruence and characterize these congruences that are complemented. In this...

Syntactic Congruences and Syntactic Algebras

Congruences of convex algebras

We provide a full description of congruence relations of convex, positive convex, and totally convex algebras. As a consequence of this result we obtain that finitely generated convex (positive convex, totally convex) algebras are finitely presentable. Convex algebras, in particular positive convex algebras, are important in the area of probabilistic systems. They are the Eilenberg-Moore algebr...

Congruences of Concept Algebras

Concept algebras are concept lattices enriched with two unary operations, a weak negation and a weak opposition. In this contribution we provide a characterization of congruences of concept algebras. AMS Mathematics Subject Classification (2000): 06B10, 06B05, 03G25, 03G10

Mal’cev Conditions from Graphs for Congruences and Tolerances

In [L4] we showed that, under certain conditions, a variety satisfies a given congruence identity if and only if it satisfies the same tolerance identity. Moreover, we mentioned that a parallel result holds for Mal’cev conditions arising from graphs. In the present note we give detailed definitions and state these more general results. The motivating example for our constructions is the followi...