Congruences on Menger 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...

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

Syntactic Congruences and Syntactic Algebras

On Congruences and Homomorphisms on Some Non-deterministic Algebras

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitab...