Pure projective modules over chain domains with Krull dimension (Q288500)

The authors establish a complete characterization of chain domains \(R\) such that every pure projective \(R\)-module is isomorphic to a direct sum of finitely presented modules. These are shown to be the chain domains \(R\) containing no idempotent 2-sided ideal \(RrR\), where \(0\neq r\in R\) is not a unit. In particular, over a chain domain with Krull dimension each pure projective module decomposes into a direct sum of finitely presented modules.