Residually finite, congruence meet-semidistributive varieties of finite type have a finite residual bound
HTML articles powered by AMS MathViewer
- by Keith A. Kearnes and Ross Willard PDF
- Proc. Amer. Math. Soc. 127 (1999), 2841-2850 Request permission
Abstract:
We show that a residually finite, congruence meet-semidistributive variety of finite type is residually $< N$ for some finite $N$. This solves Pixley’s problem and a special case of the restricted Quackenbush problem.References
- Kirby A. Baker, Finite equational bases for finite algebras in a congruence-distributive equational class, Advances in Math. 24 (1977), no. 3, 207–243. MR 447074, DOI 10.1016/0001-8708(77)90056-1
- Gábor Czédli, A characterization for congruence semidistributivity, Universal algebra and lattice theory (Puebla, 1982) Lecture Notes in Math., vol. 1004, Springer, Berlin, 1983, pp. 104–110. MR 716177, DOI 10.1007/BFb0063432
- Alfred L. Foster and Alden F. Pixley, Semi-categorical algebras. II, Math. Z. 85 (1964), 169–184. MR 168509, DOI 10.1007/BF01110374
- David Hobby and Ralph McKenzie, The structure of finite algebras, Contemporary Mathematics, vol. 76, American Mathematical Society, Providence, RI, 1988. MR 958685, DOI 10.1090/conm/076
- Wilfrid Hodges, Model theory, Encyclopedia of Mathematics and its Applications, vol. 42, Cambridge University Press, Cambridge, 1993. MR 1221741, DOI 10.1017/CBO9780511551574
- Kalle Kaarli and Alden Pixley, Affine complete varieties, Algebra Universalis 24 (1987), no. 1-2, 74–90. MR 921532, DOI 10.1007/BF01188385
- K. Kearnes and Á. Szendrei, The relationship between two commutators, to appear in Internat. J. Algebra Comput.
- P. Lipparini, A characterization of varieties with a difference term, II: neutral $=$ meet semidistributive, Canad. Math. Bull. 41 (1998), 318–327.
- Ralph McKenzie, The residual bounds of finite algebras, Internat. J. Algebra Comput. 6 (1996), no. 1, 1–28. MR 1371732, DOI 10.1142/S0218196796000027
- Robert W. Quackenbush, Equational classes generated by finite algebras, Algebra Universalis 1 (1971/72), 265–266. MR 294222, DOI 10.1007/BF02944989
- Walter Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33–53. MR 314726, DOI 10.1007/BF02945005
- R. Willard, A finite basis theorem for residually finite congruence meet-semidistributive varieties, to appear in J. Symbolic Logic.
Additional Information
- Keith A. Kearnes
- Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
- MR Author ID: 99640
- Email: kearnes@louisville.edu
- Ross Willard
- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- Email: rdwillar@gillian.math.uwaterloo.ca
- Received by editor(s): January 6, 1998
- Published electronically: June 17, 1999
- Additional Notes: The second author gratefully acknowledges the support of the NSERC of Canada.
- Communicated by: Lance W. Small
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2841-2850
- MSC (1991): Primary 08B26, 08B10
- DOI: https://doi.org/10.1090/S0002-9939-99-05097-2
- MathSciNet review: 1636966