Representing quantum structures as near semirings

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Representing quantum structures as near semirings

Original language description

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.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GF15-34697L" target="_blank" >GF15-34697L: New perspectives on residuated posets</a><br>

Continuities

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

Publication year

2016

Confidentiality

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

Name of the periodical

Logic Journal of Interest Group in Pure and Applied Logics

ISSN

1367-0751

e-ISSN

—

Volume of the periodical

24

Issue of the periodical within the volume

5

Country of publishing house

GB - UNITED KINGDOM

Number of pages

24

Pages from-to

719-742

UT code for WoS article

000390303200004

EID of the result in the Scopus database

—