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Constructions over tournaments

Jaroslav Ježek

Czechoslovak Mathematical Journal (2003)

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

Abstract

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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

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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

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  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

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