Existence of cube terms in finite algebras
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438457" target="_blank" >RIV/00216208:11320/21:10438457 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0H.d4Pj-Js" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=0H.d4Pj-Js</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-020-00700-7" target="_blank" >10.1007/s00012-020-00700-7</a>
Alternative languages
Result language
angličtina
Original language name
Existence of cube terms in finite algebras
Original language description
We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at most N, where the number N depends on the arities of basic operations of the algebra and the size of the basic set. For finite idempotent algebras we give a tight bound on N that, in the special case of algebras with more than ((vertical bar A vertical bar)(2)) basic operations, improves an earlier result of K. Kearnes and a. Szendrei. On the algorithmic side, we show that deciding the existence of cube terms is in P for idempotent algebras and in EXPTIME in general. Since an algebra contains a k-ary near unanimity operation if and only if it contains a k-dimensional cube term and generates a congruence distributive variety, our algorithm also lets us decide whether a given finite algebra has a near unanimity operation.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algebra Universalis
ISSN
0002-5240
e-ISSN
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Volume of the periodical
82
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
29
Pages from-to
11
UT code for WoS article
000610553000002
EID of the result in the Scopus database
2-s2.0-85099356936