Varieties of orthomodular lattices related to states

Mayet, R.

doi:10.1007/bf01195144

Search citation statements

Order By: Relevance

Paper Sections

Select...

Varieties Of Orthomodular Lattices Related To States2

Introduction2

Basic Notions1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1986

2015

Publication Types

Select...

Article9

Relationship

Self Cite0

Independent9

Authors

Journals

Cited by 26 publications

(22 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[15]). We claim, leaving the details to be checked by the reader, that the diagram below presents an orthomodular lattice L such that L ∈ L and L is not unital (see also [12], §VIII).…”

Section: Basic Notionsmentioning

confidence: 99%

Orthomodular lattices with state-separated noncompatible pairs

Mayet

Pták

2000

Czechoslovak Mathematical Journal

View full text Add to dashboard Cite

“…[15]). We claim, leaving the details to be checked by the reader, that the diagram below presents an orthomodular lattice L such that L ∈ L and L is not unital (see also [12], §VIII).…”

Section: Basic Notionsmentioning

confidence: 99%

Orthomodular lattices with state-separated noncompatible pairs

Mayet

Pták

2000

Czechoslovak Mathematical Journal

View full text Add to dashboard Cite

“…In this section we apply generalized regulators to the problem posed in [9]; among others, we prove that there is a continuum of varieties of OMLs with rich state spaces.…”

Section: Varieties Of Orthomodular Lattices Related To Statesmentioning

confidence: 99%

“…In particular, OM U (K) = OM R 0 (K) is the class of OMLs admitting unital sets of K-valued states. The classes OM R r (K) are varieties [9]. For each L ∈ OM U (K), the set {r ∈ I : L ∈ OM R r (K)} has a greatest element, i R (L), called the index of richness of L. (The original term used in [9] was index of strength.)…”

Section: Varieties Of Orthomodular Lattices Related To Statesmentioning

confidence: 99%

Orthomodular lattices with rich state spaces

Mayet

Navara

Rogalewicz

2000

Algebra Universalis

View full text Add to dashboard Cite

We introduce a new construction technique for orthomodular lattices. In contrast to the preceding constructions, it admits rich spaces of states (= probability measures), i.e., for each pair of incomparable elements a, c there is a state s such that s(a) = 1 > s(c). This allowed a progress in many questions that were open for a long time; among others we prove that there is a continuum of varieties of orthomodular lattices with rich state spaces and solve a problem formulated by R. Mayet in 1985. As a by-product of this research, the uniqueness problem for bounded observables (posed by S. Gudder in 1966) has been solved. As a tool, we introduce also a new construction -identification of atoms in an orthomodular lattice -which may be of separate interest.

show abstract

“…Common open problems of these structures are the characterization of classes of algebras admitting some special types of states [10,20] and the internalization in an algebraic structure of the concept of state [6,17].…”

Section: Introductionmentioning

confidence: 99%