| Title:
|
Constructions over tournaments (English) |
| Author:
|
Ježek, J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
413-428 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
tournament |
| Keyword:
|
variety |
| Keyword:
|
projective algebra |
| MSC:
|
05C20 |
| MSC:
|
08B30 |
| idZBL:
|
Zbl 1021.05041 |
| idMR:
|
MR1983462 |
| . |
| Date available:
|
2009-09-24T11:02:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127810 |
| . |
| Reference:
|
[1] R. Freese, J. Ježek and J. B. Nation: Free Lattices. Mathematical Surveys and Monographs. Vol. 42.Amer. Math. Soc., Providence, 1995. MR 1319815 |
| Reference:
|
[2] E. Fried: Tournaments and non-associative lattices.Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 151–164. MR 0321837 |
| Reference:
|
[3] E. Fried: Non-finitely based varieties of weakly associative lattices.Algebra Universalis (to appear). |
| Reference:
|
[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, 10.1016/S0012-365X(99)00155-7 |
| Reference:
|
[5] J. Ježek, P. Marković, M. Maróti and R. McKenzie: The variety generated by tournaments.Acta Univ. Carolinae 40 (1999), 21–41. MR 1728276 |
| Reference:
|
[6] J. Ježek, R. McKenzie: The variety generated by equivalence algebras.Algebra Universalis 45 (2001), 211–220. MR 1810549, 10.1007/s00012-001-8162-z |
| Reference:
|
[7] B. Jónsson: Algebras whose congruence lattices are distributive.Math. Scand. 21 (1967), 110–121. MR 0237402, 10.7146/math.scand.a-10850 |
| Reference:
|
[8] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Vol. I.Wadsworth & Brooks/Cole, Monterey, CA, 1987. MR 0883644 |
| Reference:
|
[9] V. Müller, J. Nešetřil and J. Pelant: .Either tournaments or algebras? Discrete Math. 11 (1975), 37–66. MR 0357207, 10.1016/0012-365X(75)90104-1 |
| . |
