The operator of relative complementation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F25%3A73633267" target="_blank" >RIV/61989592:15310/25:73633267 - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/epdf/10.1142/S1793557125500093" target="_blank" >https://www.worldscientific.com/doi/epdf/10.1142/S1793557125500093</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793557125500093" target="_blank" >10.1142/S1793557125500093</a>

Result language
angličtina
Original language name
The operator of relative complementation
Original language description
By the operator of relative complementation is meant a mapping assigning to every element x of an interval [a, b] of a lattice L the set x(ab) of all relative complements of x in [a, b]. Of course, if L is relatively complemented then x(ab) is nonempty for each interval [a, b] and every element x belonging to it. We study the question under what condition a complement of x in L induces a relative complement of x in [a, b]. It is well-known that this is the case provided L is modular and complemented. However, we present a more general result. Further, we investigate properties of the operator of relative complementation, in particular in the case when the interval [a, b] is a modular sublattice of L or if it is finite. Moreover, we characterize when the operator (ab) of relative complementation satisfies the identity (x(ab))(ab) approximate to x provided [a, b] is complemented and we show a class of lattices where this identity holds. Finally, we establish sufficient conditions under which two different complements of a given element x of [a, b] induce the same relative complement of x in this interval.
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
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF24-14386L" target="_blank" >GF24-14386L: Representations of algebraic semantics for substructural logics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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