| Title:
|
Quasiequational theories of flat algebras (English) |
| Author:
|
Ježek, J. |
| Author:
|
Maróti, M. |
| Author:
|
McKenzie, R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
665-675 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely $q$-based (possess a finite basis for their quasiequations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely $q$-based. (English) |
| Keyword:
|
quasiequation |
| Keyword:
|
flat algebra |
| MSC:
|
08B05 |
| MSC:
|
08C15 |
| idZBL:
|
Zbl 1081.08014 |
| idMR:
|
MR2153090 |
| . |
| Date available:
|
2009-09-24T11:26:24Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128010 |
| . |
| Reference:
|
[1] J. Lawrence and R. Willard: On finitely based groups and nonfinitely based quasivarieties.J. Algebra 203 (1998), 1–11. MR 1620693, 10.1006/jabr.1997.7470 |
| Reference:
|
[2] R. McKenzie: The residual bounds of finite algebras.Internat. J. Alg. Comput. 6 (1996), 1–28. Zbl 0844.08009, MR 1371732, 10.1142/S0218196796000027 |
| Reference:
|
[3] R. McKenzie: The residual bound of a finite algebra is not computable.Internat. J. Alg. Comput. 6 (1996), 29–48. Zbl 0844.08010, MR 1371733, 10.1142/S0218196796000039 |
| Reference:
|
[4] R. McKenzie: Tarski’s finite basis problem is undecidable.Internat. J. Alg. Comput. 6 (1996), 49–104. Zbl 0844.08011, MR 1371734, 10.1142/S0218196796000040 |
| Reference:
|
[5] R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Vol. I.Wadsworth & Brooks/Cole, Monterey, 1987. MR 0883644 |
| Reference:
|
[6] D. Pigozzi: Finite basis theorems for relatively congruence-distributive quasivarieties.Transactions of the AMS 310 (1988), 499–533. Zbl 0706.08009, MR 0946222, 10.1090/S0002-9947-1988-0946222-1 |
| . |
