Orthocomplemented difference lattices in association with generalized rings.

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00197812" target="_blank" >RIV/68407700:21230/12:00197812 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2478/s12175-012-0064-3" target="_blank" >http://dx.doi.org/10.2478/s12175-012-0064-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/s12175-012-0064-3" target="_blank" >10.2478/s12175-012-0064-3</a>

Result language
angličtina
Original language name
Orthocomplemented difference lattices in association with generalized rings.
Original language description
Orthocomplemented difference lattices (ODLs) are orthocomplemented lattices endowed with an additional operation of "abstract symmetric difference". In studying ODLs as universal algebras or instances of quantum logics, several results have been obtained(see the references at the end of this paper where the explicite link with orthomodularity is discussed, too). Since the ODLs are "nearly Boolean", a natural question arises whether there are "nearly Boolean rings" associated with ODLs. In this paper wefind such an association - we introduce some difference ring-like algebras (the DRAs) that allow for a natural one-to-one correspondence with the ODLs. The DRAs are defined by only a few rather plausible axioms. The axioms guarantee, among others, thata DRA is a group and that the association with ODLs agrees, for the subrings of DRAs, with the famous Stone (Boolean ring) correspondence.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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