Krull-Schmidt theorems in dimension 1
Lawrence S. Levy, Charles J. Odenthal · Transactions of the American Mathematical Society · 1996
Let Λ \Lambda be a semiprime, module-finite algebra over a commutative noetherian ring R R of Krull dimension 1. We find necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated Λ \Lambda -modules, and necessary and sufficient conditions for the Krull-Schmidt theorem to hold for all finitely generated torsionfree Λ \Lambda -modules (called “ Λ \Lambda -lattices” in integral representation theory, and “maximal Cohen-Macaulay modules” in the dimension-one situation in commutative algebra).