Monoids of torsion-free modules over rings with finite representation type (Q412556)

If \(R\) is a local ring, then the set \(\tau (R)\) of isomorphism classes of finitely generated torsion-free \(R\)-modules is a monoid with the operation \([M]+[N]=[M\oplus N]\). The aim of the paper is to determine all monoids that can occur as \(\tau (R)\) for one-dimensional local ring-orders \(R\) with finite representation type. A Krull-Remak-Schmidt theorem for finitely generated torsion-free modules over such rings \(R\) is also obtained.