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.
@article{119040,
author = {Ladislav Bican},
title = {Weak Krull-Schmidt theorem},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {39},
year = {1998},
pages = {633-643},
zbl = {1060.16501},
mrnumber = {1715454},
language = {en},
url = {http://dml.mathdoc.fr/item/119040}
}
Bican, Ladislav. Weak Krull-Schmidt theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 633-643. http://gdmltest.u-ga.fr/item/119040/
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