# Weak Krull-Schmidt theorem

Commentationes Mathematicae Universitatis Carolinae (1998)

- Volume: 39, Issue: 4, page 633-643
- ISSN: 0010-2628

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topBican, Ladislav. "Weak Krull-Schmidt theorem." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 633-643. <http://eudml.org/doc/248257>.

@article{Bican1998,

abstract = {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.},

author = {Bican, Ladislav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {monogeny class; epigeny class; weak Krull-Schmidt theorem; hereditary torsion theory; uniform module; co-uniform module; monogeny classes; epigeny classes; weak Krull-Schmidt theorem; hereditary torsion theories; uniform modules; co-uniform modules},

language = {eng},

number = {4},

pages = {633-643},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Weak Krull-Schmidt theorem},

url = {http://eudml.org/doc/248257},

volume = {39},

year = {1998},

}

TY - JOUR

AU - Bican, Ladislav

TI - Weak Krull-Schmidt theorem

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1998

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 39

IS - 4

SP - 633

EP - 643

AB - 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.

LA - eng

KW - monogeny class; epigeny class; weak Krull-Schmidt theorem; hereditary torsion theory; uniform module; co-uniform module; monogeny classes; epigeny classes; weak Krull-Schmidt theorem; hereditary torsion theories; uniform modules; co-uniform modules

UR - http://eudml.org/doc/248257

ER -

## References

top- Bican L., Kepka T., Němec P., Rings, Modules and Preradicals, Marcel Dekker New York, Longman Scientific Publishing, London (1982). (1982) MR0655412
- Bican L., Torrecillas B., QTAG torsionfree modules, Comment. Math. Univ. Carolinae 33 (1994), 1-20. (1994) MR1173740
- Facchini A., Krull-Schmidt fails for serial modules, Trans. Amer. Math. Soc. 348 (1996), 4561-4575. (1996) Zbl0868.16003MR1376546
- Golan J.S., Torsion Theories, Pitman Monographs and Surveys in Pure and Appl. Math. Longman Scientific Publishing, London (1986). (1986) Zbl0657.16017MR0880019
- Herbera D., Shamsuddin A., Modules with semi-local endomorphism rings, Proc. Amer. Math. Soc. 123 (1995), 3593-3600. (1995) MR1277114
- Stenström B., Rings of Quotients, Springer Berlin (1975). (1975) MR0389953
- Varadarajan K., Dual Goldie dimension, Comm. Algebra 7 (1979), 565-610. (1979) Zbl0487.16020MR0524269
- Facchini A., Module Theory. Endomorphism rings and direct decompositions in some classes of modules (Lecture Notes), to appear. MR1634015

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