Displaying similar documents to “A remark on λ -regular orthomodular lattices”

Orthomodular lattices that are horizontal sums of Boolean algebras

Ivan Chajda, Helmut Länger (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The paper deals with orthomodular lattices which are so-called horizontal sums of Boolean algebras. It is elementary that every such orthomodular lattice is simple and its blocks are just these Boolean algebras. Hence, the commutativity relation plays a key role and enables us to classify these orthomodular lattices. Moreover, this relation is closely related to the binary commutator which is a term function. Using the class ℋ of horizontal sums of Boolean algebras, we establish an identity...

On interval homogeneous orthomodular lattices

Anna de Simone, Mirko Navara, Pavel Pták (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

An orthomodular lattice L is said to be interval homogeneous (resp. centrally interval homogeneous) if it is σ -complete and satisfies the following property: Whenever L is isomorphic to an interval, [ a , b ] , in L then L is isomorphic to each interval [ c , d ] with c ≤ a and d ≥ b (resp. the same condition as above only under the assumption that all elements a , b , c , d are central in L ). Let us denote by Inthom (resp. Inthom c ) the class of all interval homogeneous orthomodular lattices (resp. centrally interval...

On interval homogeneous orthomodular lattices

Anna de Simone, Mirko Navara, Pavel Pták (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

An orthomodular lattice L is said to be interval homogeneous (resp. centrally interval homogeneous) if it is σ -complete and satisfies the following property: Whenever L is isomorphic to an interval, [ a , b ] , in L then L is isomorphic to each interval [ c , d ] with c ≤ a and d ≥ b (resp. the same condition as above only under the assumption that all elements a , b , c , d are central in L ). Let us denote by Inthom (resp. Inthom c ) the class of all interval homogeneous orthomodular lattices (resp. centrally interval...

On the structure of numerical event spaces

Gerhard Dorfer, Dietmar W. Dorninger, Helmut Länger (2010)

Kybernetika

Similarity:

The probability p ( s ) of the occurrence of an event pertaining to a physical system which is observed in different states s determines a function p from the set S of states of the system to [ 0 , 1 ] . The function p is called a numerical event or multidimensional probability. When appropriately structured, sets P of numerical events form so-called algebras of S -probabilities. Their main feature is that they are orthomodular partially ordered sets of functions p with an inherent full set of states....

On BPI Restricted to Boolean Algebras of Size Continuum

Eric Hall, Kyriakos Keremedis (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product 2 ( ω ) the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of 2 ( ω ) to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean...

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice L C V ( K ) of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a P κ -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras,...