Tolerance extensions in distributive lattices
Tolerances and congruences on lattices
Topologies in atomic quantum logics
Two extension theorems. Modular functions on complemented lattices
We prove an extension theorem for modular functions on arbitrary lattices and an extension theorem for measures on orthomodular lattices. The first is used to obtain a representation of modular vector-valued functions defined on complemented lattices by measures on Boolean algebras. With the aid of this representation theorem we transfer control measure theorems, Vitali-Hahn-Saks and Nikodým theorems and the Liapunoff theorem about the range of measures to the setting of modular functions on complemented...
Two-valued states on a concrete logic and the additivity problem
Uniform binary geometries.
Unions of uniquely complemented lattices
In this paper we generalize a result of V. N. Salij concerning direct product decompositions of lattices which are complete and uniquely complemented.
Uniqueness of bounded observables
Vector measures on the closed subspaces of a Hilbert space
Verbände von Kernen der Abbildungen, die orthogonaltreu sind
Weak congruences of an algebra with the CEP and the WCIP
Here we consider the weak congruence lattice of an algebra with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.
Zur Konstruktion vollständiger Polaritätsverbände.
-interpolation lattice-ordered groups
In [1], Jakubík showed that the class of -interpolation lattice-ordered groups forms a radical class, but left open the question of whether the class forms a torsion class. In this paper, we show that this class does indeed form a torsion class.
Делимая оболочка и ортопополнение решеточно упорядоченных модулей
Дополнения в структуре конгруeнций
Ортомодулярные частично упорядоченные множества с размерностью
Полугруппы, структура подполугрупп которых есть структура с дополнениями