Mathematicae General Algebra and Applications 22(2) (2002)
Ivan Chajda and Radomír Halas
Palacký University of Olomouc
Department of Algebra and Geometry
Tomkova 40, CZ-77900 Olomouc
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.
I. Chajda and K. Głazek, A Basic Course on General Algebra, Technical University Press, Zielona Góra
A. Day, A characterization of modularity for congruence lattices of algebras , Canad. Math. Bull. 12
B. Jónsson, On the representation of lattices , Math. Scand. 1 (1953), 193-206.
Received 18 March 2002