Weak congruences of an algebra with the CEP and the WCIP

Abstract

Here we consider the weak congruence lattice \(C_W (A)\) of an algebra \(A\) with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.