14 citations · 66 across the 12 of their papers we have counts for
14 papers
Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures
Anatolij Dvurečenskij, Omid Zahiri
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebra…
Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots
Anatolij Dvurečenskij, Omid Zahiri
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, we continue to study the structure of pseudo MV-algebras with square ro…
Morphisms on -algebras and Their Applications
Anatolij Dvurečenskij, Omid Zahiri
For a new class of algebras, called -algebras, every idempotent element determines an -algebra which is important for the structure of the -algebra. Therefore, in…
Riesz space-valued states on pseudo MV-algebras
Anatolij Dvurečenskij
We introduce Riesz space-valued states, called -states, on a pseudo MV-algebra, where is a Riesz space with a fixed strong unit . Pseudo MV-algebras are a non-com…
Sum of Observables on MV-Effect Algebras
Anatolij Dvurečenskij
Using a one-to-one correspondence between observables and their spectral resolutions, we introduce the sum of any two bounded observables of a -MV-effect algebra. This sum is co…
Quantum Observables and Effect Algebras
Anatolij Dvurečenskij
We study observables on monotone -complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. The set of sharp ele…
Olson Order of Quantum Observables
Anatolij Dvurečenskij
Using ideas of Olson \cite{Ols} who showed that the system of effect operators of a Hilbert space can be ordered by the so-called spectral order such that the system of effect oper…
Lexicographic Pseudo MV-algebras
Anatolij Dvurečenskij
A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an interval in the lexicographic product of a linear unital group with an arbitrary -group. We present c…
Pseudo MV-algebras and Lexicographic Product
Anatolij Dvurečenskij
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital -group and an -group that is not necessary Abeli…
On a New Construction of Pseudo BL-Algebras
Anatolij Dvurečenskij
We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop . Using two injective mappings from one set, ,…
Representable Effect Algebras and Observables
Anatolij Dvurečenskij
We introduce a class of monotone -complete effect algebras, called representable, which are -homomorphic images of a class of monotone -complete effect algebras of functio…
-perfect Pseudo MV-algebras and Their Representations
Anatolij Dvurečenskij
We study -perfect pseudo MV-algebras, that is, algebras which can be split into a system of ordered slices indexed by the elements of an subgroup of the grou…
Representation of States on Effect-Tribes and Effect Algebras by Integrals
Anatolij Dvurečenskij
We describe -additive states on effect-tribes by integrals. Effect-tribes are monotone -complete effect algebras of functions where operations are defined by points. Then we…
Every State on Interval Effect Algebra is Integral
Anatolij Dvurečenskij
We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel -algebra of a compact Hausdorff simplex…