  This paper is lead by the question whether there is a nice structure theory
of finitely generated modules over the Iwasawa algebra, i.e. the completed
group algebra, R of a p-adic analytic group G. For G without any p-torsion
element we prove that R is an Auslander regular ring. This result enables us to
give a good definition for pseudo-null R-modules. Then the category of
R-modules up to pseudo-isomorphisms is studied and we obtain a weak structure
theorem for the p-primary part of a finitely generated R-module. A local
duality theorem as well as the Auslander-Buchsbaum equality are further main
issues. The arithmetic applications to the Iwasawa theory of abelian varieties
are published elsewhere.
