Presentations over HNP rings with enough invertible ideals and torsionfree cancellation over neoclassical orders

AbstractWe prove a uniqueness theorem for presentations of modules over a class of hereditary noetherian prime rings that includes the hereditary orders studied in integral representation theory. The result also generalizes the elementary divisor theorem for non-commutative PIDs.A key part of the proof is an extension of a direct sum cancellation theorem of Drozd to torsionfree modules over a class of non-commutative rings that need not be module finite over their center