Weak bases in modular lattices
Weak congruences of an algebra with the CEP and the WCIP
Here we consider the weak congruence lattice of an algebra 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.
When does an AB5* module have finite hollow dimension?
Using a lattice-theoretical approach we find characterizations of modules with finite uniform dimension and of modules with finite hollow dimension.