Orthosystems of submodules of a module
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00373294" target="_blank" >RIV/68407700:21230/23:00373294 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1080/00927872.2022.2164008" target="_blank" >https://doi.org/10.1080/00927872.2022.2164008</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2022.2164008" target="_blank" >10.1080/00927872.2022.2164008</a>
Alternative languages
Result language
angličtina
Original language name
Orthosystems of submodules of a module
Original language description
Let M be a module over a ring. We first introduce a certain algebraic sub-system Sigma of the lattice of all submodules of M (an orthosystem of submod-ules). We then show that any ortholattice can be represented as a Sigma for a suitable module. Next, we introduce linear (resp. pre-Hilbert) ortholattices as those ortholattices that allow for a "linear" representation sigma (resp. for a meet-preserving "linear" representation sigma). These notions involve a type of splitting property of sigma. As an important example, we show that any Boolean algebra is pre-Hilbertian. We then find that linear orthosystems are orthomodular and that they satisfy the ortho-Arguesian law. In the rest, we consider complete orthosystems. We show that each complete orthosystem can be induced by an orthogonality relation &updatedExpOTTOM; on M. If (M, &updatedExpOTTOM;) is a linear orthospace on M then the collection of all &updatedExpOTTOM;-closed submodules is a complete orthosystem, and vice versa. Finally, we address a natural model theoretic question on the axiomati-zation of orthomodular orthosystems.& mdash;The results obtained may contribute to the algebraic foundation of quantum theory.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF20-09869L" target="_blank" >GF20-09869L: The many facets of orthomodularity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Algebra
ISSN
0092-7872
e-ISSN
1532-4125
Volume of the periodical
51
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
12
Pages from-to
2460-2471
UT code for WoS article
000913102800001
EID of the result in the Scopus database
2-s2.0-85146701980