Abstract:Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz\'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.
Keywords: congruence schemes, majority algebra, tolerance lattice, 0-conditions
AMS Subject Classification: Primary 08A10, 08A30; Secondary 06D15