Displaying similar documents to “Об обобщенных полурешетках и m -степенях индексных множеств.”

Join-semilattices with two-dimensional congruence amalgamation

Friedrich Wehrung (2002)

Colloquium Mathematicae

Similarity:

We say that a ⟨∨,0⟩-semilattice S is conditionally co-Brouwerian if (1) for all nonempty subsets X and Y of S such that X ≤ Y (i.e. x ≤ y for all ⟨x,y⟩ ∈ X × Y), there exists z ∈ S such that X ≤ z ≤ Y, and (2) for every subset Z of S and all a, b ∈ S, if a ≤ b ∨ z for all z ∈ Z, then there exists c ∈ S such that a ≤ b ∨ c and c ≤ Z. By restricting this definition to subsets X, Y, and Z of less than κ elements, for an infinite cardinal κ, we obtain the definition of a conditionally κ-co-Brouwerian...

α -filters and α -order-ideals in distributive quasicomplemented semilattices

Ismael Calomino, Sergio A. Celani (2021)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We introduce some particular classes of filters and order-ideals in distributive semilattices, called α -filters and α -order-ideals, respectively. In particular, we study α -filters and α -order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through α -order-ideals.

The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Pavel Růžička (2017)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We attach to each 〈 0 , ∨ 〉 -semilattice S a graph G S whose vertices are join-irreducible elements of S and whose edges correspond to the reflexive dependency relation. We study properties of the graph G S both when S is a join-semilattice and when it is a lattice. We call a 〈 0 , ∨ 〉 -semilattice S particle provided that the set of its join-irreducible elements satisfies DCC and join-generates S . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary...