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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1003,
author = {Ivan Chajda},
title = {Modyfications of Cs\'ak\'any's Theorem},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {20},
year = {2000},
pages = {37-41},
zbl = {0971.08002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1003}
}
Ivan Chajda. Modyfications of Csákány's Theorem. Discussiones Mathematicae - General Algebra and Applications, Tome 20 (2000) pp. 37-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1003/
[000] [1] I. Chajda and J. Duda, Compact universal relation in varieties with constants, Czechoslovak Math. J. 47 (1997), 173-178. | Zbl 0897.08007
[001] [2] B. Csákány, Varieties whose algebras have no idempotent elements, Colloq. Math. 35 (1976), 201-203. | Zbl 0331.08002
[002] [3] J. Kollár, Congruences and one-element subalgebras, Algebra Universalis 9 (1979), 266-267. | Zbl 0407.08002