Constructions over tournaments

Jaroslav Ježek

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 2, page 413-428
  • ISSN: 0011-4642

Abstract

top
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.

How to cite

top

Ježek, Jaroslav. "Constructions over tournaments." Czechoslovak Mathematical Journal 53.2 (2003): 413-428. <http://eudml.org/doc/30787>.

@article{Ježek2003,
abstract = {We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.},
author = {Ježek, Jaroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {tournament; variety; projective algebra; tournament; variety; projective algebra},
language = {eng},
number = {2},
pages = {413-428},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Constructions over tournaments},
url = {http://eudml.org/doc/30787},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Ježek, Jaroslav
TI - Constructions over tournaments
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 413
EP - 428
AB - We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.
LA - eng
KW - tournament; variety; projective algebra; tournament; variety; projective algebra
UR - http://eudml.org/doc/30787
ER -

References

top
  1. Free Lattices. Mathematical Surveys and Monographs. Vol.  42, Amer. Math. Soc., Providence, 1995. (1995) MR1319815
  2. Tournaments and non-associative lattices, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 151–164. (1970) MR0321837
  3. Non-finitely based varieties of weakly associative lattices, Algebra Universalis (to appear). (to appear) 
  4. 10.1016/S0012-365X(99)00155-7, Discrete Math. 211 (2000), 243–248. (2000) MR1735338DOI10.1016/S0012-365X(99)00155-7
  5. The variety generated by tournaments, Acta Univ. Carolinae 40 (1999), 21–41. (1999) MR1728276
  6. 10.1007/s00012-001-8162-z, Algebra Universalis 45 (2001), 211–220. (2001) MR1810549DOI10.1007/s00012-001-8162-z
  7. 10.7146/math.scand.a-10850, Math. Scand. 21 (1967), 110–121. (1967) MR0237402DOI10.7146/math.scand.a-10850
  8. Algebras, Lattices, Varieties, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA, 1987. (1987) MR0883644
  9. 10.1016/0012-365X(75)90104-1, Either tournaments or algebras? Discrete Math. 11 (1975), 37–66. (1975) MR0357207DOI10.1016/0012-365X(75)90104-1

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.