n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616646" target="_blank" >RIV/61989592:15310/22:73616646 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0165011421003195" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011421003195</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2021.08.027" target="_blank" >10.1016/j.fss.2021.08.027</a>

Jazyk výsledku

angličtina

Název v původním jazyce

n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

Popis výsledku v původním jazyce

This article is a continuation of our research on a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on lexicographic types of quantum structures which started in Dvurečenskij and Lachman (https://doi.org/10.1016/j.fss.2021.05.005). There we presented the main properties of n-dimensional spectral resolutions and observables, and we studied in depth characteristic points which are crucial for our study. Here we present the main body of our research. We investigate a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions with values in a lexicographic form of quantum structures such as 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 of spectral resolutions we have more characteristic points. The results obtained are applied to the existence of an n-dimensional meet joint observable of n one-dimensional observables on a perfect MV-algebra and a sum of n-dimensional observables.

Název v anglickém jazyce

n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. II. One-to-one correspondence

Popis výsledku anglicky

This article is a continuation of our research on a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on lexicographic types of quantum structures which started in Dvurečenskij and Lachman (https://doi.org/10.1016/j.fss.2021.05.005). There we presented the main properties of n-dimensional spectral resolutions and observables, and we studied in depth characteristic points which are crucial for our study. Here we present the main body of our research. We investigate a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions with values in a lexicographic form of quantum structures such as 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 of spectral resolutions we have more characteristic points. The results obtained are applied to the existence of an n-dimensional meet joint observable of n one-dimensional observables on a perfect MV-algebra and a sum of n-dimensional observables.

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

26

Strana od-do

17-42

Kód UT WoS článku

000813335800002

EID výsledku v databázi Scopus

2-s2.0-85114998241