On Boolean ranges of Banaschewski functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383773" target="_blank" >RIV/00216208:11320/18:10383773 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00012-018-0489-9" target="_blank" >https://doi.org/10.1007/s00012-018-0489-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-018-0489-9" target="_blank" >10.1007/s00012-018-0489-9</a>

Result language
angličtina
Original language name
On Boolean ranges of Banaschewski functions
Original language description
We construct a countable lattice S isomorphic to a bounded sublattice of the subspace lattice of a vector space with two non-isomorphic maximal Boolean sublattices. We represent one of them as the range of a Banaschewski function and we prove that this is not the case of the other. Hereby we solve a problem of F. Wehrung. We study coordinatizability of the lattice S. We prove that although it does not contain a 3-frame, the lattice S is coordinatizable. We show that the two maximal Boolean sublattices correspond to maximal Abelian regular subalgebras of the coordinatizating ring.
Czech name
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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
10101 - Pure mathematics

Project
<a href="/en/project/GA14-15479S" target="_blank" >GA14-15479S: Representation Theory (Structural Decompositions and Their Constraints)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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