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Free trees and the optimal bound in Wehrung's theorem

Pavel Růžička (2008)

Fundamenta Mathematicae

We prove that there is a distributive (∨,0,1)-semilattice of size ℵ₂ such that there is no weakly distributive (∨,0)-homomorphism from C o n c A 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...

Indecomposable matrices over a distributive lattice

Yi Jia Tan (2006)

Czechoslovak Mathematical Journal

In this paper, the concepts of indecomposable matrices and fully indecomposable matrices over a distributive lattice L are introduced, and some algebraic properties of them are obtained. Also, some characterizations of the set F n ( L ) of all n × n fully indecomposable matrices as a subsemigroup of the semigroup H n ( L ) of all n × n Hall matrices over the lattice L are given.

Lattices of relative colour-families and antivarieties

Aleksandr Kravchenko (2007)

Discussiones Mathematicae - General Algebra and Applications

We consider general properties of lattices of relative colour-families and antivarieties. Several results generalise the corresponding assertions about colour-families of undirected loopless graphs, see [1]. Conditions are indicated under which relative colour-families form a lattice. We prove that such a lattice is distributive. In the class of lattices of antivarieties of relation structures of finite signature, we distinguish the most complicated (universal) objects. Meet decompositions in lattices...

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