Commutator equations
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Commutator equations
Original language description
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].
Czech name
—
Czech description
—
Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Algebra and Computation
ISSN
0218-1967
e-ISSN
1793-6500
Volume of the periodical
34
Issue of the periodical within the volume
8
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
1273-1291
UT code for WoS article
001388147900005
EID of the result in the Scopus database
—