Krull-Schmidt Theorems in Dimension 1 

by Lawrence S. Levy and Charles J. Odenthal 

KEYWORDS 
        Krull-Schmidt, unique decompositions 
DATE 
        10/13/95 
STATUS 
        Accepted. To appear in Trans. Amer. Math. Soc. 
COMMENT 
        Typset in AMS-Latex 2.09 No graphics other than Latex pictures. 



Abstract

Let $\Lambda$ be a semiprime, module-finite algebra over a commutative 
noetherian ring $R$ of Krull dimension 1. We find necessary and sufficient 
conditions for the Krull-Schmidt theorem to hold for all finitely generated 
$\Lambda$-modules, and necessary and sufficient conditions for the 
Krull-Schmidt theorem to hold for all finitely generated torsionfree 
$\Lambda$-modules (called ``$\Lambda$-lattices'' in integral representation 
theory, and ``maximal Cohen-Macaulay modules'' in the dimension-one situation 
in commutative algebra).