Representing quantum structures as near semirings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33161672" target="_blank" >RIV/61989592:15310/16:33161672 - isvavai.cz</a>

Výsledek na webu

<a href="https://academic.oup.com/jigpal/article-lookup/doi/10.1093/jigpal/jzw031" target="_blank" >https://academic.oup.com/jigpal/article-lookup/doi/10.1093/jigpal/jzw031</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/jigpal/jzw031" target="_blank" >10.1093/jigpal/jzw031</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Representing quantum structures as near semirings

Popis výsledku v původním jazyce

In this article, we introduce the notion of near semiring with involution. Generalizing the theory of semirings we aim at represent quantum structures, such as basic algebras and orthomodular lattices, in terms of near semirings with involution. In particular, after discussing several properties of near semirings, we introduce the so-called Lukasiewicz near semirings, as a particular case of near semirings, and we show that every basic algebra is representable as (precisely, it is term equivalent to) a near semiring. In the particular case in which a Lukasiewicz near semiring is also a semiring, we obtain as a corollary a representation of MV-algebras as semirings. Analogously, by introducing a particular subclass of Lukasiewicz near semirings, that we termed orthomodular near semirings, we obtain a representation of orthomodular lattices. In the second part of the article, we discuss several universal algebraic properties of Lukasiewicz near semirings and we show that the variety of involutive integral near semirings is a Church variety. This yields a neat equational characterization of central elements of this variety. As a byproduct of such, we obtain several direct decomposition theorems for this class of algebras.

Název v anglickém jazyce

Representing quantum structures as near semirings

Popis výsledku anglicky

In this article, we introduce the notion of near semiring with involution. Generalizing the theory of semirings we aim at represent quantum structures, such as basic algebras and orthomodular lattices, in terms of near semirings with involution. In particular, after discussing several properties of near semirings, we introduce the so-called Lukasiewicz near semirings, as a particular case of near semirings, and we show that every basic algebra is representable as (precisely, it is term equivalent to) a near semiring. In the particular case in which a Lukasiewicz near semiring is also a semiring, we obtain as a corollary a representation of MV-algebras as semirings. Analogously, by introducing a particular subclass of Lukasiewicz near semirings, that we termed orthomodular near semirings, we obtain a representation of orthomodular lattices. In the second part of the article, we discuss several universal algebraic properties of Lukasiewicz near semirings and we show that the variety of involutive integral near semirings is a Church variety. This yields a neat equational characterization of central elements of this variety. As a byproduct of such, we obtain several direct decomposition theorems for this class of algebras.

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

<a href="/cs/project/GF15-34697L" target="_blank" >GF15-34697L: Nové přístupy k reziduovaným posetům</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Logic Journal of Interest Group in Pure and Applied Logics

ISSN

1367-0751

e-ISSN

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Svazek periodika

24

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

24

Strana od-do

719-742

Kód UT WoS článku

000390303200004

EID výsledku v databázi Scopus

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