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Characterizations of Hamiltonian algebras. (English) Zbl 0778.08001
An algebra \(A\) is Hamiltonian if each of its subalgebras is a congruence class of some congruence on \(A\). If \(A\) is an algebra with a nullary operation, then \(A\) is Hamiltonian iff it satisfies two simple conditions formulated in a unary algebraic function and a binary polynomial. If, moreover, \(A\) is \(n\)-permutable then only one of these conditions is necessary.
Reviewer: I.Chajda (Přerov)

08A30 Subalgebras, congruence relations
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[1] Chajda I.: Lattices of compatible relations. Arch. Math. (Brno) 13 (1977), 89-96. · Zbl 0372.08002 · eudml:17940
[2] Chajda I., Rachůnek J.: Relational characterization of permutable and \(n\)-permutable varieties. Czech. Math. J. 33 (1983), 505-508. · Zbl 0545.08011 · eudml:13408
[3] Hagemann J., Mitschke A.: On \(n\)-permutable congruences. Algebra Univ. 3 (1973), 8-12. · Zbl 0273.08001 · doi:10.1007/BF02945100
[4] Klukovits L.: Hamiltonian varieties of universal algebras. Acta Sci. Math. (Szeged) 37 (1975), 11-15. · Zbl 0285.08004
[5] Kiss E. W.: Each Hamilton variety has the congruence extension property. Algebra Univ. 12 (1981), 395-398. · Zbl 0422.08003 · doi:10.1007/BF02483899
[6] Mal’cev A. I.: On the general theory of algebraic systems. Matem. Sbornik 35 (1954), 3-20. ()
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