Geodesic
Strongly Abelian Varieties and the Hamiltonian Property
Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 331-346

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1991-019-6
Mots-clés : 08A05:, 03C05 
Kiss, E.; Valeriote, M. Strongly Abelian Varieties and the Hamiltonian Property. Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 331-346. doi: 10.4153/CJM-1991-019-6
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[1] 1. Berman, J. and McKenzie, R., Clones satisfying the term condition, Discrete Mathematics 52(1984),7–29. Google Scholar

[2] 2. Burns, Stanley and Sankappanavar, H.P.,/\ course in universal algebra. Springer-Verlag, 1981. Google Scholar

[3] 3. Hart, B. and Valeriote, M., A structure theorem for strongly abelian varieties with few models, accepted by theJSL, 1990. Google Scholar

[4] 4. Hobby, David and McKenzie, Ralph, The structure of finite algebras, Contemporary Mathematics, American Mathematical Society 76(1988). Google Scholar

[5] 5. Klukovits, L., Hamiltonian varieties of universal algebras, Acta. Sci. Math. 37(1975) :11–15. Google Scholar

[6] 6. McKenzie, R., Finite forbidden lattices, Universal Algebra and Lattice Theory 1004 Springer Lecture Notes. Springer-Verlag, 1983. Google Scholar

[7] 7. McKenzie, R., Congruence extension, Hamiltonian and Abelian properties in locally finite varieties, to appear in Algebra Universalis, 1989. Google Scholar

[8] 8. McKenzie, Ralph, McNulty, George, and Walter Taylor, Algebras, lattices, varieties Volume 1. Wadsworth and Brooks/Cole, Monterey, California, 1987. Google Scholar

[9] 9. McKenzie, Ralph and Valeriote, Matthew. The structure of locally finite decidable varieties. Birkhàuser, Boston, 1989. Google Scholar

[10] 10. Plonka, J., Diagonal algebras, Fund. Math. 58(1966),309–322. Google Scholar

[11] 11. Quackenbush, R., Quasi-afftne algebras, Algebra Universalis 20(1985), 318–327. Google Scholar

[12] 12. Shapiro, Jacob, Finite algebras with Abelian properties, PhD thesis, University of California, Berkeley, 1985. Google Scholar

[13] 13. Shapiro, Jacob, Finite algebras with Abelian properties, Algebra Universalis 25(1988), 334–364. Google Scholar

[14] 14. Valeriote, M., Finite simple Abelian algebras are strictly simple, Proc. of the Amer. Math. Soc. 108(1990), 49–57. Google Scholar

[15] 15. Valeriote, M. and Willard, R., The isomorphism problem for strongly Abelian varieties, preprint, 1989. Google Scholar

[16] 16. Valeriote, Matthew, On Decidable Locally Finite Varieties. PhD thesis, University of California, Berkeley, 1986. Google Scholar

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