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Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 131-139
DOI: https://doi.org/10.7151/dmgaa.1052

CONGRUENCE SUBMODULARITY

Ivan Chajda and Radomír Halas

Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ-77900 Olomouc
e-mail: chajda@risc.upol.cz
e-mail: halas@aix.upol.cz

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: congruence lattice, modularity, congruence k-submodularity.

2000 Mathematics Subject Classification: 08A30, 08B05, 08B10.

References

[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.

Received 18 March 2002