Taylor term does not imply any nontrivial linear one-equality Maltsev condition

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Taylor term does not imply any nontrivial linear one-equality Maltsev condition

Popis výsledku v původním jazyce

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&apos;s equation systems cannot be compressed into just one equation.

Název v anglickém jazyce

Taylor term does not imply any nontrivial linear one-equality Maltsev condition

Popis výsledku anglicky

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&apos;s equation systems cannot be compressed into just one equation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

—

Svazek periodika

80

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

9

Strana od-do

—

Kód UT WoS článku

000457680200003

EID výsledku v databázi Scopus

2-s2.0-85062427851