Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Lawrence and R. Willard: On finitely based groups and nonfinitely based quasivarieties. J. Algebra 203 (1998), 1–11.
R. McKenzie: The residual bounds of finite algebras. Internat. J. Alg. Comput. 6 (1996), 1–28.
R. McKenzie: The residual bound of a finite algebra is not computable. Internat. J. Alg. Comput. 6 (1996), 29–48.
R. McKenzie: Tarski's finite basis problem is undecidable. Internat. J. Alg. Comput. 6 (1996), 49–104.
R. McKenzie, G. McNulty and W. Taylor: Algebras, Lattices, Varieties, Vol. I. Wadsworth & Brooks/Cole, Monterey, 1987.
D. Pigozzi: Finite basis theorems for relatively congruence-distributive quasivarieties. Transactions of the AMS 310 (1988), 499–533.
Author information
Authors and Affiliations
Additional information
The first author was partially supported by the grant # 201/02/0594 of the Grant Agency of the Czech Republic, and by the Institutional grant MSM0021620839; the second author was partially supported by the grant No. Tn37877 of the Hungarian National Foundation for Scientific Research (OTHA); the third author was supported by the NSF grant # DMS-9971352.
Rights and permissions
About this article
Cite this article
Jezek, J., Maroti, M. & McKenzie, R. Quasiequational Theories of Flat Algebras. Czech Math J 55, 665–675 (2005). https://doi.org/10.1007/s10587-005-0053-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-005-0053-6