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Two finitely generated varieties
having no infinite simple members

Author: Ross Willard
Journal: Proc. Amer. Math. Soc. 126 (1998), 629-635
MSC (1991): Primary 08B26
MathSciNet review: 1458270
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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 [Enhancements On Off] (What's this?)

  • 1. D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemp. Math., vol. 76, Amer. Math. Soc. (Providence, R.I.), 1988. MR 89m:08001
  • 2. R. McKenzie, The residual bounds of finite algebras, Int. J. Algebra and Computation 6 (1996), 1-28. MR 97e:08002a
  • 3. R. McKenzie, G. McNulty and W. Taylor, Algebras, Lattices, Varieties. Vol. I, Wadsworth & Brooks/Cole (Monterey, CA), 1987. MR 88e:08001
  • 4. M. Valeriote, A residually small, finitely generated, semi-simple variety which is not residually finite, Int. J. Algebra and Computation 6 (1996), 563-569. MR 97h:08005
  • 5. R. Willard, On McKenzie's method, Periodica Math. Hungarica 32 (1996), 149-165. CMP 97:01

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Additional Information

Ross Willard
Affiliation: Department of Pure Mathematics University of Waterloo Waterloo, Ontario, Canada N2L 3G1

Keywords: Variety, finitely generated, simple, semisimple
Received by editor(s): October 26, 1995
Additional Notes: The support of the NSERC of Canada is gratefully acknowledged.
Communicated by: Lance W. Small
Article copyright: © Copyright 1998 American Mathematical Society

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