Commutator equations
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489652" target="_blank" >RIV/00216208:11320/24:10489652 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DpIjiQoIn3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DpIjiQoIn3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218196724500541" target="_blank" >10.1142/S0218196724500541</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Commutator equations
Popis výsledku v původním jazyce
In this paper, we investigate properties of varieties of algebras described by a novel concept of equation that we call commutator equation. A commutator equation is a relaxation of the standard term equality obtained substituting the equality relation with the commutator relation. Namely, an algebra A satisfies the commutator equation pALMOST EQUAL TOCq if for each congruence θ in Con(A) and for each substitution pA,qA of elements in the same θ-class, we have (pA,qA)ELEMENT OF[θ,θ]. This notion of equation draws inspiration from the definition of a weak difference term and allows for further generalization of it. Furthermore, we present an algorithm that establishes a connection between congruence equations valid in the variety generated by the abelian algebras of the idempotent reduct of a given variety and congruence equations that hold in the entire variety. Additionally, we provide a proof that if the variety generated by the abelian algebras of the idempotent reduct of a variety satisfies a nontrivial idempotent Mal'cev condition, then also the entire variety satisfies a nontrivial idempotent Mal'cev condition, a statement that follows also from [12, Theorem 3.13].
Název v anglickém jazyce
Commutator equations
Popis výsledku anglicky
In this paper, we investigate properties of varieties of algebras described by a novel concept of equation that we call commutator equation. A commutator equation is a relaxation of the standard term equality obtained substituting the equality relation with the commutator relation. Namely, an algebra A satisfies the commutator equation pALMOST EQUAL TOCq if for each congruence θ in Con(A) and for each substitution pA,qA of elements in the same θ-class, we have (pA,qA)ELEMENT OF[θ,θ]. This notion of equation draws inspiration from the definition of a weak difference term and allows for further generalization of it. Furthermore, we present an algorithm that establishes a connection between congruence equations valid in the variety generated by the abelian algebras of the idempotent reduct of a given variety and congruence equations that hold in the entire variety. Additionally, we provide a proof that if the variety generated by the abelian algebras of the idempotent reduct of a variety satisfies a nontrivial idempotent Mal'cev condition, then also the entire variety satisfies a nontrivial idempotent Mal'cev condition, a statement that follows also from [12, Theorem 3.13].
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
International Journal of Algebra and Computation
ISSN
0218-1967
e-ISSN
1793-6500
Svazek periodika
34
Číslo periodika v rámci svazku
8
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
19
Strana od-do
1273-1291
Kód UT WoS článku
001388147900005
EID výsledku v databázi Scopus
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