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ArticleOriginal scientific text

Title

Congruence submodularity

Authors 1, 1

Affiliations

  1. Palacký University of Olomouc, Department of Algebra and Geometry, Tomkova 40, CZ-77900 Olomouc

Abstract

We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.

Keywords

ENG
congruence lattice, modularity, congruence k-submodularity

Bibliography

  1. I. Chajda and K. Głazek, A Basic Course on General Algebra, Technical University Press, Zielona Góra (Poland), 2000.
  2. A. Day, A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull. 12 (1969), 167-173.
  3. B. Jónsson, On the representation of lattices, Math. Scand. 1 (1953), 193-206.
Discussiones Mathematicae - General Algebra and Applications
2002/22/2
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Pages:
131-139
Main language of publication
English
Received
2002-03-18
Published
2002

DOI: 10.7151/dmgaa.1052

Exact and natural sciences