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Discussiones Mathematicae General Algebra and Applications 20(1) (2000) 37-41
DOI: https://doi.org/10.7151/dmgaa.1003

MODIFICATIONS OF CSÁKÁNY'S THEOREM

Ivan Chajda

Department of Algebra and Geometry, Palacký University of Olomouc
Tomkova 40, Cz-779 00 Olomouc, Czech Republic
e-mail: :chajda@risc.upol.cz

Abstract

Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.

Keywords: congruence class, idempotent element, permutable variety, Mal'cev condition.

1991 Mathematics Subject Classification: 8B05, 08A30.

References

[1]	I. Chajda and J. Duda, Compact universal relation in varieties with constants, Czechoslovak Math. J. 47 (1997), 173-178.
[2]	B. Csákány, Varieties whose algebras have no idempotent elements, Colloq. Math. 35 (1976), 201-203.
[3]	J. Kollár, Congruences and one-element subalgebras, Algebra Universalis 9 (1979), 266-267.

Received 12 December 1997
Revised 28 December 1998