Discussiones
Mathematicae General Algebra and Applications 22(2) (2002)
131139
doi: 10.7151/dmgaa.1052
CONGRUENCE SUBMODULARITY
Ivan Chajda and Radomír Halas
Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ77900 Olomouc
email: chajda@risc.upol.cz
email: 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
4submodularity, 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 ksubmodularity.
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), 167173.

[3]
B. Jónsson, On the representation of lattices , Math. Scand. 1 (1953), 193206.

Received 18 March 2002