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Locally solvable factors of varieties

Author(s): Keith A. Kearnes
Journal: Proc. Amer. Math. Soc. 124 (1996), 3619-3625.
MSC (1991): Primary 08B25; Secondary 08A05
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Abstract: We give necessary and sufficient local conditions, which are easy to check, for a locally finite variety $\cal V$ to decompose as the product of a locally solvable subvariety $\cal U$ and a subvariety $\cal W$ which has type set disjoint from the type set of $\cal U$ .

References:

1.: P. Agliano and K. A. Kearnes, Congruence semimodular varieties I: locally finite varieties, Algebra Universalis 32 (1994), 224-269. MR 95i:08010
2.: R. Freese and R. McKenzie, Commutator Theory for Congruence Modular Varieties, LMS Lecture Notes v. 125, Cambridge University Press, 1987. MR 89c:08006
3.: D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics v. 76, American Mathematical Society, 1988. MR 89m:08001
4.: K. A. Kearnes, A Hamiltonian property for nilpotent algebras, to appear in Algebra Universalis.
5.: R. McKenzie and M. Valeriote, The Structure of Decidable Locally Finite Varieties, Progress in Mathematics v. 79, Birkhäuser, 1989. MR 92j:08001
6.: M. Valeriote, On Decidable Locally Finite Varieties, Ph. D. Dissertation, U. C. Berkeley, 1986.

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Additional Information:

Keith A. Kearnes
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Email: kearnes@comp.uark.edu

DOI: 10.1090/S0002-9939-96-03501-0
PII: S 0002-9939(96)03501-0
Received by editor(s): September 7, 1994
Received by editor(s) in revised form: June 5, 1995
Additional Notes: Research supported by a fellowship from the Alexander von Humboldt Stiftung.
Communicated by: Lance W. Small
Copyright of article: Copyright 1996, American Mathematical Society


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