A geometric approach to universal quasigroup identities
Archivum Mathematicum (1993)
- Volume: 029, Issue: 1-2, page 97-103
- ISSN: 0044-8753
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topHavel, Václav J.. "A geometric approach to universal quasigroup identities." Archivum Mathematicum 029.1-2 (1993): 97-103. <http://eudml.org/doc/247448>.
@article{Havel1993,
abstract = {In the present paper we construct the accompanying identity $\hat\{I\}$ of a given quasigroup identity $I$. After that we deduce the main result: $I$ is isotopically invariant (i.e., for every guasigroup $Q$ it holds that if $I$ is satisfied in $Q$ then $I$ is satisfied in every quasigroup isotopic to $Q$) if and only if it is equivalent to $\hat\{I\}$ (i.e., for every quasigroup $Q$ it holds that in $Q$ either $I, \hat\{I\}$ are both satisfied or both not).},
author = {Havel, Václav J.},
journal = {Archivum Mathematicum},
keywords = {3-webs and their coordinatizing quasigroups; isotopic quasigroups and loops; identities invariant under isotopies; accompanying identities; 3-webs; coordinatizing quasigroups; isotopic quasigroups; accompanying identity; quasigroup identity; isotopically invariant},
language = {eng},
number = {1-2},
pages = {97-103},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A geometric approach to universal quasigroup identities},
url = {http://eudml.org/doc/247448},
volume = {029},
year = {1993},
}
TY - JOUR
AU - Havel, Václav J.
TI - A geometric approach to universal quasigroup identities
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 97
EP - 103
AB - In the present paper we construct the accompanying identity $\hat{I}$ of a given quasigroup identity $I$. After that we deduce the main result: $I$ is isotopically invariant (i.e., for every guasigroup $Q$ it holds that if $I$ is satisfied in $Q$ then $I$ is satisfied in every quasigroup isotopic to $Q$) if and only if it is equivalent to $\hat{I}$ (i.e., for every quasigroup $Q$ it holds that in $Q$ either $I, \hat{I}$ are both satisfied or both not).
LA - eng
KW - 3-webs and their coordinatizing quasigroups; isotopic quasigroups and loops; identities invariant under isotopies; accompanying identities; 3-webs; coordinatizing quasigroups; isotopic quasigroups; accompanying identity; quasigroup identity; isotopically invariant
UR - http://eudml.org/doc/247448
ER -
References
top- On universal quasigroup identities, Mathematica Bohemica 117 (1992), 20-32. (1992) MR1154051
- Identical relation in loops, I, Journ. Austral. Math. Soc. 12 (1971), 275-286. (1971) MR0297915
- Isotopy invariants in quasigroups, Trans. Amer. Math. Soc. 151 (1970), 511-526. (1970) Zbl0209.04701MR0272932
- Introduction to the theory of algebras with hyperidentities, (in Russian), Erevan, 1986. MR0877518
- Algebraic nets and quasigroups, (in Russian), Kishinev, 1971.
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