An invariant of modules on submodules of a free module
by
Barbara L. Osofsky
Rutgers University

The author has previously defined two related ordinal invariants on a subclass of the class of all modules over a ring. Here she discusses one of them applied to submodules of free modules over a (n \aleph₀-) coherent ring. This invariant, l'(M) is defined by

1. l'(M) <= 0 <===> M is a direct sum of finitely generated modules; and
2. l'(M) <= \kappa <===> M = \sum_{\alpha in \Omega} N_\alpha where each N_\alpha is finitely generated, \Omega is an ordinal, and l'(N_\alpha \cap \sum_{\beta < \alpha}) < \kappa for all \alpha in \Omega.

Date received: March 17, 1999