One of the most useful results in modular representation theory of finite groups is Green's indecomposability theorem [4]. In order to state it in a simple form, let us fix a complete discrete valuation ring [Oscr ] of characteristic 0 with algebraically closed residue field [ ] of characteristic p≠0. Unless stated otherwise, all our modules will be free of finite rank over [Oscr ] or [ ], respectively. In its most popular form, Green's theorem says the following.