n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. I. Characteristic points

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73609901" target="_blank" >RIV/61989592:15310/22:73609901 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011421001858" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011421001858</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2021.05.005" target="_blank" >10.1016/j.fss.2021.05.005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. I. Characteristic points

Popis výsledku v původním jazyce

In the paper, we investigate a one-to-one correspondence between $n$-dimensional observables and $n$-dimensional spectral resolutions with values in a kind of a lexicographic form of quantum structures like perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is $k$-perfect for $k&gt;1$, then even for the two-dimensional case we have more characteristic points. The obtained results are also applied to existence of an $n$-dimensional meet joint observable of $n$ one-dimensional observables on a perfect MV-algebra. The results are divided into two parts. In Part I, we present notions of $n$-dimensional observables and $n$-dimensional spectral resolutions with accent on lexicographic type effect algebras and lexicographic MV-algebras. We concentrate on characteristic points of spectral resolutions and the main body is in Part II where one-to-one relations between observables and spectral resolutions are presented.

Název v anglickém jazyce

n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. I. Characteristic points

Popis výsledku anglicky

In the paper, we investigate a one-to-one correspondence between $n$-dimensional observables and $n$-dimensional spectral resolutions with values in a kind of a lexicographic form of quantum structures like perfect MV-algebras or perfect effect algebras. The multidimensional version of this problem is more complicated than a one-dimensional one because if our algebraic structure is $k$-perfect for $k&gt;1$, then even for the two-dimensional case we have more characteristic points. The obtained results are also applied to existence of an $n$-dimensional meet joint observable of $n$ one-dimensional observables on a perfect MV-algebra. The results are divided into two parts. In Part I, we present notions of $n$-dimensional observables and $n$-dimensional spectral resolutions with accent on lexicographic type effect algebras and lexicographic MV-algebras. We concentrate on characteristic points of spectral resolutions and the main body is in Part II where one-to-one relations between observables and spectral resolutions are presented.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-09869L" target="_blank" >GF20-09869L: Ortomodularita z různých pohledů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

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

1872-6801

Svazek periodika

442

Číslo periodika v rámci svazku

SI

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

1-16

Kód UT WoS článku

000813335800001

EID výsledku v databázi Scopus

2-s2.0-85107327283