Previous |  Up |  Next


tournament; variety; projective algebra
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.
[1] R.  Freese, J. Ježek and J. B. Nation: Free Lattices. Mathematical Surveys and Monographs. Vol.  42. Amer. Math. Soc., Providence, 1995. MR 1319815
[2] E.  Fried: Tournaments and non-associative lattices. Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 151–164. MR 0321837
[3] E. Fried: Non-finitely based varieties of weakly associative lattices. Algebra Universalis (to appear).
[4] J.  Ježek, P.  Marković, M.  Maróti and R.  McKenzie: Equations of tournaments are not finitely based. Discrete Math. 211 (2000), 243–248. MR 1735338
[5] J.  Ježek, P.  Marković, M.  Maróti and R.  McKenzie: The variety generated by tournaments. Acta Univ. Carolinae 40 (1999), 21–41. MR 1728276
[6] J.  Ježek, R.  McKenzie: The variety generated by equivalence algebras. Algebra Universalis 45 (2001), 211–220. MR 1810549
[7] B.  Jónsson: Algebras whose congruence lattices are distributive. Math. Scand. 21 (1967), 110–121. MR 0237402
[8] R.  McKenzie, G.  McNulty and W.  Taylor: Algebras, Lattices, Varieties, Vol. I. Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644
[9] V.  Müller, J.  Nešetřil and J.  Pelant: Either tournaments or algebras? Discrete Math. 11 (1975), 37–66. MR 0357207
Partner of
EuDML logo