Subdirect products and propagating equations with an application to the Moufang Theorem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10509656" target="_blank" >RIV/00216208:11320/24:10509656 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i4meQKls93" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=i4meQKls93</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.26493/2590-9770.1715.3ef" target="_blank" >10.26493/2590-9770.1715.3ef</a>
Alternative languages
Result language
angličtina
Original language name
Subdirect products and propagating equations with an application to the Moufang Theorem
Original language description
We introduce the concept of propagating equations and focus on the case of associativity propagating in varieties of loops.An equation ε propagates in an algebra X if ε(-RIGHTWARDS ARROWy ) holds whenever ε(-RIGHTWARDS ARROWx ) holds and the elements of -RIGHTWARDS ARROWy are contained in the subalgebra of X generated by -RIGHTWARDS ARROWx . If ε propagates in X then it propagates in all subalgebras and products of X but not necessarily in all homomorphic images of X. If V is a variety, the propagating core V[ε] = {X ELEMENT OF V :ε propagates in X} is a quasivariety but not necessarily a variety. We prove by elementary means Goursat's Lemma for loops and describe all subdirect products of Xk and all finitely generated loops in HSP(X) for a nonabelian simple loopX. If V is a variety of loops in which associativity propagates, X is a finite loop in whichassociativity propagates and every subloop of X is either nonabelian simple or contained in V, then associativity propagates in HSP(X) LOGICAL OR V. We study the propagating core S[x(yz)=(xy)z] of Steiner loops with respect to associativity. While this is not a variety, we exhibit many varieties contained in S[x(yz)=(xy)z], each providing a solution to Rajah's problem, i.e., a variety of loops not contained in Moufang loops in which the Moufang Theorem holds.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LTAUSA19070" target="_blank" >LTAUSA19070: Commutators, quasigroups and Yang Baxter equation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>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
The Art of Discrete and Applied Mathematics
ISSN
2590-9770
e-ISSN
2590-9770
Volume of the periodical
7
Issue of the periodical within the volume
3
Country of publishing house
SI - SLOVENIA
Number of pages
20
Pages from-to
nestránkováno
UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-85213223251