Triangular scheme for congruence distributivity
by
Ivan Chajda
Palacky University Olomouc, Dept. of Algebra and Geometry
Coauthors: G.Czedli, E.Horvath

We introduce a Triangular scheme for congruences which is satisfied in any congruence distributive algebra. We show that for a congruence permutable algebra A, the Scheme is equivalent to distributivity of ConA. A more general Triangular Principle is shown to be equivalent to distributivity of ConA for any algebra A. We present also the so-called Trapezoid scheme characterizing congruence distributivity of a variety V and, in particular case, direct decomposability of congruences in an algebra A. The Triangular scheme is modofied to characterize congruence semimodularity of A and congruence distributivity of the lattice of congruence kernels.

Date received: January 21, 2003