Two finitely generated varieties having no infinite simple members
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- by Ross Willard PDF
- Proc. Amer. Math. Soc. 126 (1998), 629-635 Request permission
Abstract:
Using a method of R. McKenzie, we construct a finitely generated semisimple variety of infinite type, and a finitely generated nonsemisimple variety of finite type, both having arbitrarily large finite but no infinite simple members. This amplifies M. Valeriote’s negative solution to Problem 11 from Hobby and McKenzie, The Structure of Finite Algebras.References
- 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
- Ralph McKenzie, The residual bounds of finite algebras, Internat. J. Algebra Comput. 6 (1996), no. 1, 1–28. MR 1371732, DOI 10.1142/S0218196796000027
- Ralph N. McKenzie, George F. McNulty, and Walter F. Taylor, Algebras, lattices, varieties. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1987. MR 883644
- Matthew A. Valeriote, A residually small, finitely generated, semi-simple variety which is not residually finite, Internat. J. Algebra Comput. 6 (1996), no. 5, 563–569. MR 1419131, DOI 10.1142/S0218196796000313
- R. Willard, On McKenzie’s method, Periodica Math. Hungarica 32 (1996), 149–165.
Additional Information
- 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): October 26, 1995
- Additional Notes: The support of the NSERC of Canada is gratefully acknowledged.
- Communicated by: Lance W. Small
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 629-635
- MSC (1991): Primary 08B26
- DOI: https://doi.org/10.1090/S0002-9939-98-04521-3
- MathSciNet review: 1458270