The aim of this lecture is to discuss properties of modular elements in
lattices and results about which lattices contain modular elements.
Conditions are found for when a lattice is (r)-connected. Intersection
lattices of central subspace arrangements with no embedded components are
shown to be l.c.m. lattices and examples are presented. It is shown that
the lattice of partial partitions has a E.L.-labeling. Thus, the lattice
of partial partitions is shellable and super solvable and its proper order
complex is collapsable.

Keywords:

Hyperplane arrangements; lattice of partial partitions; l.c.m. lattices.

Lecture #10725

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