Direct sum cancellation for modules over one-dimensional rings

Abstract

Let R be a one-dimensional Noetherian domain with finite normalization R. In the eighties the second-named author and S. Wiegand developed a mechanism for studying the cancellation problem for finitely generated torsion-free R-modules. The key idea, described in [Wie84] and [WW87], is to represent a given torsion-free module M as a pullback: M −→ RM ↓ ↓ M/fM −→ RM/fM ∗This research was initiated while the author was a visitor at the University of Nebraska, supported by the Fonds zur Forderung der wissenschaftlichen Forschung. †Partially supported by grants from the National Science Foundation, the National Security Agency and the Mathematical Sciences Research Institute, where much of this research was done.