Lattices of subspaces of vector space with orthogonality

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603116" target="_blank" >RIV/61989592:15310/20:73603116 - isvavai.cz</a>
Result on the web
<a href="https://obd.upol.cz/id_publ/333183002" target="_blank" >https://obd.upol.cz/id_publ/333183002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0219498820500413" target="_blank" >10.1142/S0219498820500413</a>

Result language
angličtina
Original language name
Lattices of subspaces of vector space with orthogonality
Original language description
It is well known that the lattice of subspaces of a vector space over a field is modular. We investigate under which conditions this lattice is orthocomplemented with respect to the orthogonality operation. Using this operation, we define closed subspaces of a vector space and study the lattice of these subspaces. In particular, we investigate when this lattice is modular or orthocomplemented. Finally, we introduce splitting subspaces as special closed subspaces and we prove that the poset of splitting subspaces and the poset of projections are isomorphic orthomodular posets. The vector spaces under consideration are of arbitrary dimension and over arbitrary fields.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

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)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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