The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F11%3A00055100" target="_blank" >RIV/00216224:14310/11:00055100 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.springerlink.com/content/t44107u38q472u54/about/" target="_blank" >http://www.springerlink.com/content/t44107u38q472u54/about/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-010-0561-7" target="_blank" >10.1007/s00500-010-0561-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states

Popis výsledku v původním jazyce

We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebras E, namely their blocks M, centers C(E), compatibility centers B(E) and sets of all sharp elements S(E) of E. We show that in every such effect algebra E, everyatomic block M and the set S(E) are bifull sub-lattice effect algebras of E. Consequently, if E is moreover sharply dominating then every atomic block M is again sharply dominating and the basic decompositions of elements (BDE of x) in E and in M coincide. Thus in the compatibility center B(E) of E, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks and in E. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely, we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebra E with B(E) not equal C(E).

Název v anglickém jazyce

The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states

Popis výsledku anglicky

We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebras E, namely their blocks M, centers C(E), compatibility centers B(E) and sets of all sharp elements S(E) of E. We show that in every such effect algebra E, everyatomic block M and the set S(E) are bifull sub-lattice effect algebras of E. Consequently, if E is moreover sharply dominating then every atomic block M is again sharply dominating and the basic decompositions of elements (BDE of x) in E and in M coincide. Thus in the compatibility center B(E) of E, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks and in E. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely, we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebra E with B(E) not equal C(E).

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Soft computing

ISSN

1432-7643

e-ISSN

—

Svazek periodika

15

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

543-555

Kód UT WoS článku

000287451000012

EID výsledku v databázi Scopus

—