Orthocomplemented difference lattices in association with generalized rings.

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00197812" target="_blank" >RIV/68407700:21230/12:00197812 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.2478/s12175-012-0064-3" target="_blank" >http://dx.doi.org/10.2478/s12175-012-0064-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/s12175-012-0064-3" target="_blank" >10.2478/s12175-012-0064-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Orthocomplemented difference lattices in association with generalized rings.

Popis výsledku v původním jazyce

Orthocomplemented difference lattices (ODLs) are orthocomplemented lattices endowed with an additional operation of "abstract symmetric difference". In studying ODLs as universal algebras or instances of quantum logics, several results have been obtained(see the references at the end of this paper where the explicite link with orthomodularity is discussed, too). Since the ODLs are "nearly Boolean", a natural question arises whether there are "nearly Boolean rings" associated with ODLs. In this paper wefind such an association - we introduce some difference ring-like algebras (the DRAs) that allow for a natural one-to-one correspondence with the ODLs. The DRAs are defined by only a few rather plausible axioms. The axioms guarantee, among others, thata DRA is a group and that the association with ODLs agrees, for the subrings of DRAs, with the famous Stone (Boolean ring) correspondence.

Název v anglickém jazyce

Orthocomplemented difference lattices in association with generalized rings.

Popis výsledku anglicky

Orthocomplemented difference lattices (ODLs) are orthocomplemented lattices endowed with an additional operation of "abstract symmetric difference". In studying ODLs as universal algebras or instances of quantum logics, several results have been obtained(see the references at the end of this paper where the explicite link with orthomodularity is discussed, too). Since the ODLs are "nearly Boolean", a natural question arises whether there are "nearly Boolean rings" associated with ODLs. In this paper wefind such an association - we introduce some difference ring-like algebras (the DRAs) that allow for a natural one-to-one correspondence with the ODLs. The DRAs are defined by only a few rather plausible axioms. The axioms guarantee, among others, thata DRA is a group and that the association with ODLs agrees, for the subrings of DRAs, with the famous Stone (Boolean ring) correspondence.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

6

Strana od-do

1063-1068

Kód UT WoS článku

000312663200004

EID výsledku v databázi Scopus

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