Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T08:53:46.620Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly Abelian Varieties and the Hamiltonian Property

Published online by Cambridge University Press:  20 November 2018

E. Kiss  and
M. Valeriote
E. Kiss
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences 1364 Budapest, P. O. Box 12 Hungary
M. Valeriote
Affiliation:
Department of Mathematics and Statistics McMaster University, HamiltonOntario L8S4K1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we show that every locally finite strongly Abelian variety satisfies the Hamiltonian property. An algebra is Hamiltonian if every one of its subuniverses is a block of some congruence of the algebra. A counterexample is provided to show that not all strongly Abelian varieties are Hamiltonian.

Keywords

08A05:03C05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 331 - 346
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Berman, J. and McKenzie, R., Clones satisfying the term condition, Discrete Mathematics 52(1984),7–29.Google Scholar
2. Burns, Stanley and Sankappanavar, H.P.,/\ course in universal algebra. Springer-Verlag, 1981.Google Scholar
3. Hart, B. and Valeriote, M., A structure theorem for strongly abelian varieties with few models, accepted by theJSL, 1990.Google Scholar
4. Hobby, David and McKenzie, Ralph, The structure of finite algebras, Contemporary Mathematics, American Mathematical Society 76(1988).Google Scholar
5. Klukovits, L., Hamiltonian varieties of universal algebras, Acta. Sci. Math. 37(1975) :11–15.Google Scholar
6. McKenzie, R., Finite forbidden lattices, Universal Algebra and Lattice Theory 1004 Springer Lecture Notes. Springer-Verlag, 1983.Google Scholar
7. McKenzie, R., Congruence extension, Hamiltonian and Abelian properties in locally finite varieties, to appear in Algebra Universalis, 1989.Google Scholar
8. McKenzie, Ralph, McNulty, George, and Walter Taylor, Algebras, lattices, varieties Volume 1. Wadsworth and Brooks/Cole, Monterey, California, 1987.Google Scholar
9. McKenzie, Ralph and Valeriote, Matthew. The structure of locally finite decidable varieties. Birkhàuser, Boston, 1989.Google Scholar
10. Plonka, J., Diagonal algebras, Fund. Math. 58(1966),309–322.Google Scholar
11. Quackenbush, R., Quasi-afftne algebras, Algebra Universalis 20(1985), 318–327.Google Scholar
12. Shapiro, Jacob, Finite algebras with Abelian properties, PhD thesis, University of California, Berkeley, 1985.Google Scholar
13. Shapiro, Jacob, Finite algebras with Abelian properties, Algebra Universalis 25(1988), 334–364.Google Scholar
14. Valeriote, M., Finite simple Abelian algebras are strictly simple, Proc. of the Amer. Math. Soc. 108(1990), 49–57.Google Scholar
15. Valeriote, M. and Willard, R., The isomorphism problem for strongly Abelian varieties, preprint, 1989.Google Scholar
16. Valeriote, Matthew, On Decidable Locally Finite Varieties. PhD thesis, University of California, Berkeley, 1986.Google Scholar