On quasigroups with the left loop property

A. Nourou Issa

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 663-669
  • ISSN: 0010-2628

Abstract

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Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.

How to cite

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Issa, A. Nourou. "On quasigroups with the left loop property." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 663-669. <http://eudml.org/doc/248611>.

@article{Issa2000,
abstract = {Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.},
author = {Issa, A. Nourou},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroups; loops; left quasigroups; left loops; left Bol identity; homogeneous loops},
language = {eng},
number = {4},
pages = {663-669},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On quasigroups with the left loop property},
url = {http://eudml.org/doc/248611},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Issa, A. Nourou
TI - On quasigroups with the left loop property
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 663
EP - 669
AB - Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.
LA - eng
KW - quasigroups; loops; left quasigroups; left loops; left Bol identity; homogeneous loops
UR - http://eudml.org/doc/248611
ER -

References

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  1. Belousov V.D., Foundations of the theory of quasigroups and loops (in Russian), Izdat. Nauka, Moscow, 1967. MR0218483
  2. Bruck R.H., Some results in the theory of quasigroups, Trans. Amer. Math. Soc. 55 (1944), 19-52. (1944) Zbl0063.00635MR0009963
  3. Bruck R.H., A Survey of Binary Systems, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1958. Zbl0141.01401MR0093552
  4. Fenyves F., Extra loops II, Publ. Math. Debrecen 16 (1969), 187-192. (1969) MR0262409
  5. Issa A.N., Gyrogroups and homogeneous loops, Reports Math. Phys. 44 (1999), 3 345-357. (1999) Zbl0953.20055MR1737383
  6. Kepka T., Commutative Moufang loops and distributive Steiner quasigroups nilpotent of class 3 , Comment. Math. Univ. Carolinae 21 (1980), 355-370. (1980) Zbl0439.20048MR0580690
  7. Kikkawa M., Geometry of homogeneous Lie loops, Hiroshima Math. J. 5 (1975), 141-179. (1975) Zbl0304.53037MR0383301
  8. Kunen K., Moufang quasigroups, J. Algebra 183 (1996), 231-234. (1996) Zbl0855.20056MR1397396
  9. Kunen K., Quasigroups, loops, and associative laws, J. Algebra 185 (1996), 194-204. (1996) Zbl0860.20053MR1409983
  10. Pflugfelder H.O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990. Zbl0715.20043MR1125767
  11. Robinson D.A., Bol loops, Trans. Amer. Math. Soc. 123 (1966), 341-354. (1966) Zbl0163.02001MR0194545
  12. Robinson D.A., Bol quasigroups, Publ. Math. Debrecen 19 (1972), 151-153. (1972) MR0325829
  13. Sabinin L.V., On the gyrogroups of Ungar, Russian Math. Surveys 50 (1995), 5 1095-1096. (1995) Zbl0865.20054MR1365062
  14. Sabinin L.V., Mikheev P.O., On the law of composition of velocities in special relativity theory, Russian Math. Surveys 48 (1993), 5 183-185. (1993) Zbl0814.53057MR1258774
  15. Ungar A.A., Thomas rotation and the parametrization of the Lorentz transformation group, Foundations Phys. Lett. 1 (1988), 1 57-89. (1988) MR0962332
  16. Ungar A.A., Thomas precession and its associated grouplike structure, Amer. J. Phys. 59 (1991), 9 824-834. (1991) MR1126776

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