The lattice of clones of self-dual operations collapsed

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471892" target="_blank" >RIV/00216208:11320/23:10471892 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=M68yeHmAWv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=M68yeHmAWv</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218196723500327" target="_blank" >10.1142/S0218196723500327</a>

Result language
angličtina
Original language name
The lattice of clones of self-dual operations collapsed
Original language description
In this paper, the authors consider the concept of homomorphic equivalence, where two clones A and B are so related if and only if there are clone homomorphisms from A to B and vice versa, and prove that there are 2ℵ0 many equivalence classes of clones of self-dual operations, operations preserving the relation {(0,1),(1,2),(0,2)}. Furthermore, clones of self-dual operations with respect to the binary relation <=Minor defined by a minor preserving map are described. The authors also discuss some minor conditions on any clones A and B such that ANEITHER LESS-THAN NOR EQUAL TOB; a minor condition that holds in A but not in B is given. In the last section, some conjectures are proposed.
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

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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