Categories of orthogonality spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00119310" target="_blank" >RIV/00216224:14310/22:00119310 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2021.106859" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106859</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106859" target="_blank" >10.1016/j.jpaa.2021.106859</a>
Alternative languages
Result language
angličtina
Original language name
Categories of orthogonality spaces
Original language description
An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a Boolean algebra. Together with the maps that preserve the Boolean substructures, we are led to the category NOS of normal orthogonality spaces. Moreover, an orthogonality space of finite rank is called linear if for any two distinct elements e and f there is a third one g such that exactly one of f and g is orthogonal to e and the pairs e, f and e, g have the same orthogonal complement. Linear orthogonality spaces arise from finite-dimensional Hermitian spaces. We are led to the full subcategory LOS of NOS and we show that the morphisms are the orthogonality-preserving lineations. Finally, we consider the full subcategory OS pound of LOS whose members arise from positive definite Hermitian spaces over Baer ordered *-fields with a Euclidean fixed field. We establish that the morphisms of OS pound are induced by generalised semiunitary mappings.
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
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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
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Pure and Applied Algebra
ISSN
0022-4049
e-ISSN
1873-1376
Volume of the periodical
226
Issue of the periodical within the volume
3
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
22
Pages from-to
106859
UT code for WoS article
000704010100011
EID of the result in the Scopus database
2-s2.0-85111757693