Some applications of atomistic algebraic lattices
by
Andreja Tepavcevic
University of Novi Sad

A codistributive element a in an atomistic algebraic lattice L has a complement a' which is distributive and both a and a' induce the same congruence on L. Algebraic consequence: If the weak congruence lattice of an algebra A is atomistic, then

- A has at least two constants;

- A is idempotent;

- each congruence on A is an extension of a congruence on a subalgebra of A;

- if A has the CIP, then also A has the CEP;

- no congruence on A has a class which is a subalgebra.

Date received: February 27, 2003