Geodesic
Modyfications of Csákány's Theorem
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 37-41
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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 
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Chajda, Ivan. Modyfications of Csákány's Theorem. Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 1, pp. 37-41. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_1_a2/

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[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.