  In the early 1990's, Lionel Schwartz gave a lovely characterization of the
Krull filtration of U, the category of unstable modules over the mod p Steenrod
algebra. Soon after, this filtration was used by the author as an
organizational tool in posing and studying some topological nonrealization
conjectures. In recent years the Krull filtration of U has been similarly used
by Castellana, Crespo, and Scherer in their study of H--spaces with finiteness
conditions, and Gaudens and Schwartz have given a proof of some of my
conjectures. In light of these topological applications, it seems timely to
better expose the algebraic properties of the Krull filtration.
