Congruence relations on direct products of lattices
Congruence Relations on the Lattice of Partitions in a Set
Congruence representations of join-homomorphisms of distributive lattices: a short proof
Congruences generated by filters
Congruences in ordered sets
A concept of congruence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
Congruences in ordered sets and LU compatible equivalences
A concept of equivalence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
Congruences on finite lattices
Connections between ideals of non-commutative generalizations of -algebras and ideals of their underlying lattices
Corrigendum to "Perfect semilattices".
Decompositions in lattices and some representations of algebras [Book]
Direct decomposability of tolerances on lattices, semilattices and quasilattices
Direct summands of Goldie extending elements in modular lattices
In this paper some results on direct summands of Goldie extending elements are studied in a modular lattice. An element of a lattice with is said to be a Goldie extending element if and only if for every there exists a direct summand of such that is essential in both and . Some characterizations of decomposition of a Goldie extending element in a modular lattice are obtained.
Directly decomposable tolerances on direct products of lattices and semilattices
Distinguishing subsets in lattices
Double -algebras with Stone congruence lattices
El Espectro Y La Dimension De Anillos En El Algebra Sobre Un Topos.
Fantastic filters of lattice implication algebras.
Flat semilattices
Frame tolerances are directly decomposable
Free trees and the optimal bound in Wehrung's theorem
We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from to with 1 in its range, for any algebra A with either a congruence-compatible structure of a (∨,1)-semi-lattice or a congruence-compatible structure of a lattice. In particular, is not isomorphic to the (∨,0)-semilattice of compact congruences of any lattice. This improves Wehrung’s solution of Dilworth’s Congruence Lattice Problem, by giving the best cardinality...