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ArticleOriginal scientific text

Title

Modyfications of Csákány's Theorem

Authors 1

Affiliations

  1. Department of Algebra and Geometry, Palacký University of Olomouc, Tomkova 40, Cz-779 00 Olomouc, Czech Republic

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

ENG
congruence class, idempotent element, permutable variety, Mal'cev condition

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2000/20/1
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Pages:
37-41
Main language of publication
English
Received
1997-12-12
Published
2000

DOI: 10.7151/dmgaa.1003

Exact and natural sciences