Hereditary Noetherian Prime Rings 2. Finitely Generated Projective Modules

Let R be a hereditary Noetherian prime ring. We determine a full set of invariants for the isomorphism class of any finitely generated projective R-module of uniform dimension at least 2. In particular we prove that P X Q X implies P Q whenever P has uniform dimension at least 2. Among the applications of these results are necessary and sufficient conditions for the existence of a bound to the number of generators needed for right ideals of R.