Geodesic
Weak Krull-Schmidt theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 633-643.

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Recently, A. Facchini [3] showed that the classical Krull-Schmidt theorem fails for serial modules of finite Goldie dimension and he proved a weak version of this theorem within this class. In this remark we shall build this theory axiomatically and then we apply the results obtained to a class of some modules that are torsionfree with respect to a given hereditary torsion theory. As a special case we obtain that the weak Krull-Schmidt theorem holds for the class of modules that are both uniform and co-uniform. A simple example shows that this generalizes the result of [3] mentioned above.
Classification : 16D70, 16S90
Keywords: monogeny class; epigeny class; weak Krull-Schmidt theorem; hereditary torsion theory; uniform module; co-uniform module 
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     title = {Weak {Krull-Schmidt} theorem},
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Bican, Ladislav. Weak Krull-Schmidt theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 633-643. http://geodesic.mathdoc.fr/item/CMUC_1998__39_4_a0/