u-Independence and quadratic u-independence in the construction of indecomposable finitely generated modules

Let R be a valuation domain having an ideal I such that a maximal immediate extension S of R contains four units u-independent over I. We construct a 4-generated indecomposable R-module M with Goldie dimension g(M) = 2. We thus supplement a result by Lunsford who constructed indecomposable finitely generated R-modules making use of sets of quadratically u-independent elements of S.