The graphs of join-semilattices and the shape of congruence lattices of particle lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369292" target="_blank" >RIV/00216208:11320/17:10369292 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.14712/1213-7243.2015.214" target="_blank" >http://dx.doi.org/10.14712/1213-7243.2015.214</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/1213-7243.2015.214" target="_blank" >10.14712/1213-7243.2015.214</a>

Result language
angličtina
Original language name
The graphs of join-semilattices and the shape of congruence lattices of particle lattices
Original language description
We attach to each < 0, V >-semilattice S a graph G(S) whose vertices are join-irreducible elements of S and whose edges correspond to the reflexive dependency relation. We study properties of the graph G(S) both when S is a join-semilattice and when it is a lattice. We call a < 0, V >-semilattice S particle provided that the set of its join-irreducible elements satisfies DCC and join-generates S. We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of the corresponding graph that are closed in a certain zero-dimensional topology. Thus we extend the result known for principally chain finite lattices.
Czech name
—
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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