States on wEMV-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603666" target="_blank" >RIV/61989592:15310/20:73603666 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs40574-020-00233-w" target="_blank" >https://link.springer.com/article/10.1007%2Fs40574-020-00233-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40574-020-00233-w" target="_blank" >10.1007/s40574-020-00233-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

States on wEMV-algebras

Popis výsledku v původním jazyce

Recently in Dvurecenskij and Zahiri (A variety containing EMV-algebras and Pierce sheaves,), new algebras called wEMV-algebras, which generalize MV-algebras, generalized Boolean algebras and EMV-algebras, were founded, and for these algebras a top element is not assumed a priori. For this class we define a state as a mapping from a wEMV-algebra into the real interval [0, 1] which preserves a kind of subtraction of two comparable elements and attaining the value 1 in some element. It can happen that some wEMV-algebras are stateless, e.g. cancellative ones. We characterize extremal states just as state-morphisms which are wEMV-homomorphisms from an algebra into the real interval [0, 1]. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal ideals having a special property. Moreover, we prove that under some conditions every state on a wEMV-algebra is a weak limit of a net of convex combinations of state-morphisms.

Název v anglickém jazyce

States on wEMV-algebras

Popis výsledku anglicky

Recently in Dvurecenskij and Zahiri (A variety containing EMV-algebras and Pierce sheaves,), new algebras called wEMV-algebras, which generalize MV-algebras, generalized Boolean algebras and EMV-algebras, were founded, and for these algebras a top element is not assumed a priori. For this class we define a state as a mapping from a wEMV-algebra into the real interval [0, 1] which preserves a kind of subtraction of two comparable elements and attaining the value 1 in some element. It can happen that some wEMV-algebras are stateless, e.g. cancellative ones. We characterize extremal states just as state-morphisms which are wEMV-homomorphisms from an algebra into the real interval [0, 1]. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal ideals having a special property. Moreover, we prove that under some conditions every state on a wEMV-algebra is a weak limit of a net of convex combinations of state-morphisms.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA

ISSN

1972-6724

e-ISSN

—

Svazek periodika

13

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

515-527

Kód UT WoS článku

000543579000001

EID výsledku v databázi Scopus

2-s2.0-85086591197