Residuated operators in complemented posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73590109" target="_blank" >RIV/61989592:15310/18:73590109 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1142/S1793557118500973" target="_blank" >http://dx.doi.org/10.1142/S1793557118500973</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S1793557118500973" target="_blank" >10.1142/S1793557118500973</a>

Result language
angličtina
Original language name
Residuated operators in complemented posets
Original language description
Using the operators of taking upper and lower cones in a poset with a unary operation, we define operators M(x, y) and R(x, y) in the sense of multiplication and residuation, respectively, and we show that by using these operators, a general modification of residuation can be introduced. A relatively pseudocomplemented poset can be considered as a prototype of such an operator residuated poset. As main results, we prove that every Boolean poset as well as every pseudo-orthomodular poset can be organized into a (left) operator residuated structure. Some results on pseudo-orthomodular posets are presented which show the analogy to orthomodular lattices and orthomodular posets.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

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

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