Geodesic
Weak Krull-Schmidt theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 4, pp. 633-643 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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 
@article{CMUC_1998_39_4_a0,
     author = {Bican, Ladislav},
     title = {Weak {Krull-Schmidt} theorem},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {633--643},
     year = {1998},
     volume = {39},
     number = {4},
     mrnumber = {1715454},
     zbl = {1060.16501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1998_39_4_a0/}
}
TY  - JOUR
AU  - Bican, Ladislav
TI  - Weak Krull-Schmidt theorem
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1998
SP  - 633
EP  - 643
VL  - 39
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMUC_1998_39_4_a0/
LA  - en
ID  - CMUC_1998_39_4_a0
ER  - 
%0 Journal Article
%A Bican, Ladislav
%T Weak Krull-Schmidt theorem
%J Commentationes Mathematicae Universitatis Carolinae
%D 1998
%P 633-643
%V 39
%N 4
%U http://geodesic.mathdoc.fr/item/CMUC_1998_39_4_a0/
%G en
%F CMUC_1998_39_4_a0
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/