Selfdistributive groupoids of small orders

Jaroslav Ježek; Tomáš Kepka

Czechoslovak Mathematical Journal (1997)

  • Volume: 47, Issue: 3, page 463-468
  • ISSN: 0011-4642

Abstract

top
After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.

How to cite

top

Ježek, Jaroslav, and Kepka, Tomáš. "Selfdistributive groupoids of small orders." Czechoslovak Mathematical Journal 47.3 (1997): 463-468. <http://eudml.org/doc/30376>.

@article{Ježek1997,
abstract = {After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.},
author = {Ježek, Jaroslav, Kepka, Tomáš},
journal = {Czechoslovak Mathematical Journal},
keywords = {distributive; medial; groupoid; left distributive groupoids; distributive medial groupoids; quasigroups},
language = {eng},
number = {3},
pages = {463-468},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Selfdistributive groupoids of small orders},
url = {http://eudml.org/doc/30376},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Ježek, Jaroslav
AU - Kepka, Tomáš
TI - Selfdistributive groupoids of small orders
JO - Czechoslovak Mathematical Journal
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 3
SP - 463
EP - 468
AB - After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.
LA - eng
KW - distributive; medial; groupoid; left distributive groupoids; distributive medial groupoids; quasigroups
UR - http://eudml.org/doc/30376
ER -

References

top
  1. Quasitrivial left distributive groupoids, Commentationes Math. Univ. Carolinae 35 (1994), 597–606. (1994) MR1321230
  2. 10.1007/BF01594185, Math. Ann. 114 (1937), 414–431. (1937) Zbl0016.22603MR1513147DOI10.1007/BF01594185
  3. Group conjugation has non-trivial LD-identities, Commentationes Math. Univ. Carolinae 35 (1994), 219–222. (1994) MR1286567
  4. 10.1147/rd.45.0460, IBM J. of Research Development 4 (1960), 460–471. (1960) Zbl0100.01803MR0123961DOI10.1147/rd.45.0460
  5. Atoms in the lattice of varieties of distributive groupoids, Colloquia Math. Soc. J. Bolyai 14. Lattice Theory, Szeged, 1974, pp. 185–194. (1974) MR0485630
  6. Distributive groupoids, Rozpravy ČSAV, Řada mat. a přír. věd 91, Academia, Praha, 1981. (1981) MR0672563
  7. [unknown], Math. Nachr. 87 (1979), Distributive division groupoids 103–107. (1979) Zbl0444.20067MR0536417
  8. Notes on quasimodules, Commentationes Math. Univ. Carolinae 20 (1979), 229–247. (1979) Zbl0413.20054MR0539554
  9. [unknown], Czech. Math. J. 31 (1981), Commutative Moufang loops and distributive groupoids of small orders 633–669. (1981) MR0631607
  10. Étude algébrique de la notion de moyenne, J. Math. Pures et Appl. 50 (1971), 53–264. (1971) Zbl0215.40401MR0291342

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.