Closure conditions of commutativity

Václav J. Havel; Josef Klouda

Archivum Mathematicum (1994)

  • Volume: 030, Issue: 1, page 9-16
  • ISSN: 0044-8753

Abstract

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There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.

How to cite

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Havel, Václav J., and Klouda, Josef. "Closure conditions of commutativity." Archivum Mathematicum 030.1 (1994): 9-16. <http://eudml.org/doc/247546>.

@article{Havel1994,
abstract = {There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.},
author = {Havel, Václav J., Klouda, Josef},
journal = {Archivum Mathematicum},
keywords = {coordinatizing quasigroups of a 3-web; 3-web closure conditions with respect to constant lines; commutative quasigroups; commutativity; quasigroups; closure conditions; 3-webs},
language = {eng},
number = {1},
pages = {9-16},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Closure conditions of commutativity},
url = {http://eudml.org/doc/247546},
volume = {030},
year = {1994},
}

TY - JOUR
AU - Havel, Václav J.
AU - Klouda, Josef
TI - Closure conditions of commutativity
JO - Archivum Mathematicum
PY - 1994
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 030
IS - 1
SP - 9
EP - 16
AB - There are investigated some closure conditions of Thomsen type in 3-webs which gurantee that at least one of coordinatizing quasigroups of a given 3-web is commutative.
LA - eng
KW - coordinatizing quasigroups of a 3-web; 3-web closure conditions with respect to constant lines; commutative quasigroups; commutativity; quasigroups; closure conditions; 3-webs
UR - http://eudml.org/doc/247546
ER -

References

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  1. Projektive Ebenen, Berlin - Heidelberg - New York, 1975. (1975) Zbl0307.50001MR0370350
  2. What is a loop?, Studies in Modern Algebra, Prentice - Hall (1963), 59-99. (1963) Zbl0199.05202MR0146228
  3. Elements of the theory of quasigroups and loops (in Russian), Kishinev, 1967. (1967) 
  4. 3-webs (in Czech), Knižnice Vys. uč. techn. (Brno) A-17 (1978), 209-242. (1978) 
  5. Closure conditions in quasigroups (in Russian), Izv. Akad. Nauk Mold. SSR (1971/3), 172. (1971/3) 
  6. Gewebe und Gruppen, Math. Ann. 114 (1937), 414-431. (1937) Zbl0016.22603MR1513147
  7. Gruppoide und Funktionalgleichungen, Berlin, 1984. (1984) MR0753469

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