Orthomodular lattices that are Z(2)-rich

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00324871" target="_blank" >RIV/68407700:21230/18:00324871 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s11587-018-0378-8" target="_blank" >http://dx.doi.org/10.1007/s11587-018-0378-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11587-018-0378-8" target="_blank" >10.1007/s11587-018-0378-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Orthomodular lattices that are Z(2)-rich

Popis výsledku v původním jazyce

We study the orthomodular lattices (OMLs) that have an abundance of Z(2)-valued states. We call these OMLs Z(2)-rich. Themotivation for the investigation comes from a natural algebraic curiosity that reflects the state of the (orthomodular) art, the consideration also has a certain bearing on the foundation of quantum theories (OMLs are often identified with " quantum logics") and mathematical logic (Z(2)-states are fundamental in mathematical logic). Before we launch on the subject proper, we observe, for a potential application elsewhere, that there can be a more economic introduction of Z(2)-richness - the Z(2)-richness in the orthocomplemented setup is sufficient to imply orthomodularity. In the further part we review basic examples of OMLs that are Z(2)-rich and that are not. Then we show, as a main result, that the Z(2)-rich OMLs form a large and algebraicly "friendly" class-they form a variety. In the appendix we note that the OMLs that allow for a natural introduction of a symmetric difference provide a source of another type of examples of Z(2)-rich OMLs. We also formulate open questions related to the matter studied.

Název v anglickém jazyce

Orthomodular lattices that are Z(2)-rich

Popis výsledku anglicky

We study the orthomodular lattices (OMLs) that have an abundance of Z(2)-valued states. We call these OMLs Z(2)-rich. Themotivation for the investigation comes from a natural algebraic curiosity that reflects the state of the (orthomodular) art, the consideration also has a certain bearing on the foundation of quantum theories (OMLs are often identified with " quantum logics") and mathematical logic (Z(2)-states are fundamental in mathematical logic). Before we launch on the subject proper, we observe, for a potential application elsewhere, that there can be a more economic introduction of Z(2)-richness - the Z(2)-richness in the orthocomplemented setup is sufficient to imply orthomodularity. In the further part we review basic examples of OMLs that are Z(2)-rich and that are not. Then we show, as a main result, that the Z(2)-rich OMLs form a large and algebraicly "friendly" class-they form a variety. In the appendix we note that the OMLs that allow for a natural introduction of a symmetric difference provide a source of another type of examples of Z(2)-rich OMLs. We also formulate open questions related to the matter studied.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Ricerche di Matematica

ISSN

0035-5038

e-ISSN

—

Svazek periodika

67

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

IT - Italská republika

Počet stran výsledku

9

Strana od-do

321-329

Kód UT WoS článku

000447409000002

EID výsledku v databázi Scopus

2-s2.0-85044459300