Locally solvable factors of varieties
Author: Keith A. Kearnes
Journal: Proc. Amer. Math. Soc. 124 (1996), 3619-3625
MSC (1991): Primary 08B25; Secondary 08A05
MathSciNet review: 1343705
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Abstract: We give necessary and sufficient local conditions, which are easy to check, for a locally finite variety to decompose as the product of a locally solvable subvariety and a subvariety which has type set disjoint from the type set of .
- 1. P. Aglianò and K. A. Kearnes, Congruence semimodular varieties. I. Locally finite varieties, Algebra Universalis 32 (1994), no. 2, 224–269. MR 1290160, https://doi.org/10.1007/BF01191540
- 2. Ralph Freese and Ralph McKenzie, Commutator theory for congruence modular varieties, London Mathematical Society Lecture Note Series, vol. 125, Cambridge University Press, Cambridge, 1987. MR 909290
- 3. David Hobby and Ralph McKenzie, The structure of finite algebras, Contemporary Mathematics, vol. 76, American Mathematical Society, Providence, RI, 1988. MR 958685
- 4. K. A. Kearnes, A Hamiltonian property for nilpotent algebras, to appear in Algebra Universalis.
- 5. Ralph McKenzie and Matthew Valeriote, The structure of decidable locally finite varieties, Progress in Mathematics, vol. 79, Birkhäuser Boston, Inc., Boston, MA, 1989. MR 1033992
- 6. M. Valeriote, On Decidable Locally Finite Varieties, Ph. D. Dissertation, U. C. Berkeley, 1986.
- P. Agliano and K. A. Kearnes, Congruence semimodular varieties I: locally finite varieties, Algebra Universalis 32 (1994), 224-269. MR 95i:08010
- R. Freese and R. McKenzie, Commutator Theory for Congruence Modular Varieties, LMS Lecture Notes v. 125, Cambridge University Press, 1987. MR 89c:08006
- D. Hobby and R. McKenzie, The Structure of Finite Algebras, Contemporary Mathematics v. 76, American Mathematical Society, 1988. MR 89m:08001
- K. A. Kearnes, A Hamiltonian property for nilpotent algebras, to appear in Algebra Universalis.
- R. McKenzie and M. Valeriote, The Structure of Decidable Locally Finite Varieties, Progress in Mathematics v. 79, Birkhäuser, 1989. MR 92j:08001
- M. Valeriote, On Decidable Locally Finite Varieties, Ph. D. Dissertation, U. C. Berkeley, 1986.
Keith A. Kearnes
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
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
Article copyright: © Copyright 1996 American Mathematical Society