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Inherently Nonfinitely Based Solvable Algebras

Published online by Cambridge University Press:  20 November 2018

Keith Kearnes  and
Ross Willard
Keith Kearnes
Affiliation:
Department of Mathematics, Harvey Mudd College Claremont, California 91711 U.S.A.
Ross Willard
Affiliation:
Department of Pure Mathematics, University of Waterloo Waterloo, Ontario N2L 3G1
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Abstract

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We prove that an inherently nonfinitely based algebra cannot generate an abelian variety. On the other hand, we show by example that it is possible for an inherently nonfinitely based algebra to generate a strongly solvable variety.

Keywords

08B05algebravarietyinherently nonfinitely basedHamiltonianstrongly solvable
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 514 - 521
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Baldwin, J. T. and Berman, J., The number of subdirectly irreducible algebras in a variety, Algebra Universalis 5(1975), 379–389.Google Scholar
2. Berman, J., Varieties with log-linear free spectra, manuscript, 1984.Google Scholar
3. Birkhoff, G., On the structure of abstract algebras, Math. Proc. Cambridge Philos. Soc. 31, 433–454.Google Scholar
4. Bryant, R., The laws of finite pointed groups, Bull. London Math. Soc. 14(1982), 119–123.Google Scholar
5. Hobby, D. and McKenzie, R., The Structure of Finite Algebras, Amer. Math. Soc, Contemporary Math. 76, Providence, Rhode Island, 1988.Google Scholar
6. Kiss, E. W., Each Hamiltonian variety has the congruence extension property, Algebra Universalis 12(1981), 395–398.Google Scholar
7. Kiss, E. W. and Valeriote, M., Abelian algebras and the Hamiltonian property, J. Pure Appl. Algebra 87(1993), 37–49.Google Scholar
8. Klukovits, L., Hamiltonian varieties of universal algebras, Acta Sci. Math. 37(1975), 11–15.Google Scholar
9. McNulty, G. F. and Shallon, C. R., Inherently nonfinitely based finite algebras. In: Universal Algebra and Lattice Theory, (eds. R. S. Freese and O. C. Garcia), Lecture Notes in Math. 1004, Springer-Verlag, 1983,206–231.Google Scholar