Frankl-Füredi type inequalities for polynomial semi-lattices.
Frankl’s conjecture for large semimodular and planar semimodular lattices
A lattice is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element such that at most half of the elements of satisfy . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let denote the number of nonzero join-irreducible elements of . It is well-known that consists of at most elements....
Frattini sublattices in varieties of lattices
Frattinian constructions
Free almost-p-lattices
Free Archimedean l-Groups.
Free bounded distributive lattice over finite ordered sets and their skeletons.
Free group automorphisms, invariant orderings and topological applications.
Free, iteratively closed categories of complete lattices
Free -groups and free products of -groups
In this paper we have given the construction of free -groups generated by a po-group and the construction of free products in any sub-product class of -groups. We have proved that the -free products satisfy the weak subalgebra property.
Free lattices over halflattices
Free -products of lattices. I
Free -products of lattices. II
Free products and elementary types of Boolean Algebras.
Free products in varieties of lattice-ordered groups
Free products of abelian -groups
Free products of lattices
Free -distributive lattice over an -element chain.
Free Suslin algebras
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...