Inversions on complete lattices and Girard quantales
Irreducibility and generation in continuous lattices.
Isomorphismen von Kontexten und Konzeptualverbänden
Isomorphismes de lattis de fermés convexes
Jednoznačnosť rozkladu sväzu na direktný súčin
Join-closed and meet-closed subsets in complete lattices
To every subset of a complete lattice we assign subsets , and define join-closed and meet-closed sets in . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.
Joins of congruences in -groups
Join-semilattices with two-dimensional congruence amalgamation
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...
Jordan-Hölder Theorem for Lines
Konvexita (1. část)
-многообразия без независимого базиса тождеств. II.
Lattice betweenness relation and a generalization of König's lemma
Lattice effect algebras densely embeddable into complete ones
An effect algebraic partial binary operation defined on the underlying set uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion of there exists an effect algebraic partial binary operation then need not be an extension of . Moreover, for an Archimedean atomic lattice effect algebra we give a necessary and sufficient condition for that existing on is an extension of defined on . Further we show that such extending exists at most...
Lattice isomorphisms of alternative algebras
Lattice operators and topologies.
Lattice ordered groups with complete epimorphic images
Lattice separation, coseparation and regular measures.
Lattice uniformities on orthomodular structures
Lattice-inadmissible incidence structures
Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure .
Lattices and semilattices having an antitone involution in every upper interval
We study -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.