Observables on perfect MV-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73590161" target="_blank" >RIV/61989592:15310/19:73590161 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011418306894" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011418306894</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2018.11.018" target="_blank" >10.1016/j.fss.2018.11.018</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Observables on perfect MV-algebras

Popis výsledku v původním jazyce

An observable on an MV-algebra is any σ-homomorphism from the Borel σ-algebra B(R) into the MV-algebra which maps a sequence of disjoint Borel sets onto summable elements of the MV-algebra. We establish that there is a one-to-one correspondence between observables on Rad-Dedekind σ-complete perfect MV-algebras with principal radicals and their spectral resolutions. It means that we show that our partial information on an observable known only on all intervals of the form (−∞,t) is sufficient to determine the whole information about the observable. In addition, this correspondence allows us to define the Olson order which is a partial order on the set O(M) of all observables on an MV-algebra M as well as, we can define a sum of observables, so that O(M) becomes a lattice-ordered semigroup.

Název v anglickém jazyce

Observables on perfect MV-algebras

Popis výsledku anglicky

An observable on an MV-algebra is any σ-homomorphism from the Borel σ-algebra B(R) into the MV-algebra which maps a sequence of disjoint Borel sets onto summable elements of the MV-algebra. We establish that there is a one-to-one correspondence between observables on Rad-Dedekind σ-complete perfect MV-algebras with principal radicals and their spectral resolutions. It means that we show that our partial information on an observable known only on all intervals of the form (−∞,t) is sufficient to determine the whole information about the observable. In addition, this correspondence allows us to define the Olson order which is a partial order on the set O(M) of all observables on an MV-algebra M as well as, we can define a sum of observables, so that O(M) becomes a lattice-ordered semigroup.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

FUZZY SETS AND SYSTEMS

ISSN

0165-0114

e-ISSN

—

Svazek periodika

369

Číslo periodika v rámci svazku

AUG

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

57-81

Kód UT WoS článku

000468735500004

EID výsledku v databázi Scopus

2-s2.0-85057591093