Ein Assoziativitätskriterium vom Foulis-Holland-Typ.
Ein Beitrag zur Theorie der Orthogonalität auf Mengen
Exotic logics
Extensions dans les treillis
Filters in partially ordered sets
Fractal construction of an atomic Archimedean effect algebra with non-atomic subalgebra of sharp elements
Does there exist an atomic Archimedean lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question is given.
Freely adjoining a complement to a lattice
Functional completeness in pseudocomplemented de Morgan algebras
-supplemented property in the lattices
Let be a lattice with the greatest element . Following the concept of generalized small subfilter, we define -supplemented filters and investigate the basic properties and possible structures of these filters.
Generalizations of Boolean algebras. An attribute exploration
Generalized difference posets and orthoalgebras.
Generalized -lattices of order ω+
Generating semigroups for complete atomistic ortholattices.
Gram-Schmidt's orthogonalization based on the concept of generalized orthogonality
Group-valued measures on coarse-grained quantum logics
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained...
“Hidden variables” on concrete logics (extensions)
Hilbert-space-valued states on quantum logics
Horizontal sums of basic algebras
The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.
Hypersubstitutions in orthomodular lattices
It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.
Implication algebras
We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unified approach enables us to compare the mentioned algebras and apply a unified treatment of congruence properties....