Displaying 41 – 60 of 85

Showing per page

On strong uniform dimension of locally finite groups

A. Sakowicz (2003)

Colloquium Mathematicae

We give the description of locally finite groups with strongly balanced subgroup lattices and we prove that the strong uniform dimension of such groups exists. Moreover we show how to determine this dimension.

On systems of congruences on principal filters of orthomodular implication algebras

Radomír Halaš, Luboš Plojhar (2007)

Mathematica Bohemica

Orthomodular implication algebras (with or without compatibility condition) are a natural generalization of Abbott’s implication algebras, an implication reduct of the classical propositional logic. In the paper deductive systems (= congruence kernels) of such algebras are described by means of their restrictions to principal filters having the structure of orthomodular lattices.

On the concreteness of quantum logics

Pavel Pták, John David Maitland Wright (1985)

Aplikace matematiky

It is shown that for any quantum logic one can find a concrete logic and a surjective homomorphism from onto such that maps the centre of onto the centre of . Moreover, one can ensure that each finite set of compatible elements in is the image of a compatible subset of . This result is “best possible” - let a logic be the homomorphic image of a concrete logic under a homomorphism such that, if is a finite subset of the pre-image of a compatible subset of , then is compatible....

On the existence of super-decomposable pure-injective modules over strongly simply connected algebras of non-polynomial growth

Stanisław Kasjan, Grzegorz Pastuszak (2014)

Colloquium Mathematicae

Assume that k is a field of characteristic different from 2. We show that if Γ is a strongly simply connected k-algebra of non-polynomial growth, then there exists a special family of pointed Γ-modules, called an independent pair of dense chains of pointed modules. Then it follows by a result of Ziegler that Γ admits a super-decomposable pure-injective module if k is a countable field.

On the Lebesgue decomposition of the normal states of a JBW-algebra

Jacques Dubois, Brahim Hadjou (1992)

Mathematica Bohemica

In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.

On the rhomboidal heredity in ideal lattices

Ladislav Beran (1992)

Commentationes Mathematicae Universitatis Carolinae

We show that the class of principal ideals and the class of semiprime ideals are rhomboidal hereditary in the class of modular lattices. Similar results are presented for the class of ideals with forbidden exterior quotients and for the class of prime ideals.

On the set representation of an orthomodular poset

John Harding, Pavel Pták (2001)

Colloquium Mathematicae

Let P be an orthomodular poset and let B be a Boolean subalgebra of P. A mapping s:P → ⟨0,1⟩ is said to be a centrally additive B-state if it is order preserving, satisfies s(a') = 1 - s(a), is additive on couples that contain a central element, and restricts to a state on B. It is shown that, for any Boolean subalgebra B of P, P has an abundance of two-valued centrally additive B-states. This answers positively a question raised in [13, Open question, p. 13]. As a consequence one obtains a somewhat...

Currently displaying 41 – 60 of 85