Taylor term does not imply any nontrivial linear one-equality Maltsev condition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10391985" target="_blank" >RIV/00216208:11320/19:10391985 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=q..FWVo86o" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=q..FWVo86o</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-019-0580-x" target="_blank" >10.1007/s00012-019-0580-x</a>
Alternative languages
Result language
angličtina
Original language name
Taylor term does not imply any nontrivial linear one-equality Maltsev condition
Original language description
It is known that any finite idempotent algebra that satisfies a nontrivial Maltsev condition must satisfy the linear one-equality Maltsev condition (a variant of the term discovered by Siggers and refined by Kearnes, Markovi, and McKenzie): We show that if we drop the finiteness assumption, the k-ary weak near unanimity equations imply only trivial linear one-equality Maltsev conditions for every k3. From this it follows that there is no nontrivial linear one-equality condition that would hold in all idempotent algebras having Taylor terms. Miroslav Olak has recently shown that there is a weakest nontrivial strong Maltsev condition for idempotent algebras. Olak has found several such (mutually equivalent) conditions consisting of two or more equations. Our result shows that Olak's equation systems cannot be compressed into just one equation.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
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
80
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
9
Pages from-to
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UT code for WoS article
000457680200003
EID of the result in the Scopus database
2-s2.0-85062427851