Examples to Birkhoff's quasigroup axioms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F16%3A71124" target="_blank" >RIV/60460709:41310/16:71124 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jalgebra.2016.07.029" target="_blank" >http://dx.doi.org/10.1016/j.jalgebra.2016.07.029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2016.07.029" target="_blank" >10.1016/j.jalgebra.2016.07.029</a>
Alternative languages
Result language
angličtina
Original language name
Examples to Birkhoff's quasigroup axioms
Original language description
The equational-variety of quasigroups is defined by six identities, called Birkhoff's identities. It is known, that only four of them suffice to define the variety; actually, there are nine different combinations of four Birkhoff's identities defining quasigroups, other four combinations define larger varieties and it was open whether the remaining two cases define quasigroups or larger classes. We solve the question here constructing examples of algebras that are not quasigroups and satisfy the open cases of Birkhoff's identities.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Algebra
ISSN
0021-8693
e-ISSN
—
Volume of the periodical
466
Issue of the periodical within the volume
N
Country of publishing house
GB - UNITED KINGDOM
Number of pages
4
Pages from-to
204-207
UT code for WoS article
000383411300013
EID of the result in the Scopus database
2-s2.0-84989926315