| Title:
|
Weak Krull-Schmidt theorem (English) |
| Author:
|
Bican, Ladislav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
633-643 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
monogeny class |
| Keyword:
|
epigeny class |
| Keyword:
|
weak Krull-Schmidt theorem |
| Keyword:
|
hereditary torsion theory |
| Keyword:
|
uniform module |
| Keyword:
|
co-uniform module |
| MSC:
|
16D70 |
| MSC:
|
16S90 |
| idZBL:
|
Zbl 1060.16501 |
| idMR:
|
MR1715454 |
| . |
| Date available:
|
2009-01-08T18:47:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119040 |
| . |
| Reference:
|
[1] Bican L., Kepka T., Němec P.: Rings, Modules and Preradicals.Marcel Dekker New York, Longman Scientific Publishing, London (1982). MR 0655412 |
| Reference:
|
[2] Bican L., Torrecillas B.: QTAG torsionfree modules.Comment. Math. Univ. Carolinae 33 (1994), 1-20. MR 1173740 |
| Reference:
|
[3] Facchini A.: Krull-Schmidt fails for serial modules.Trans. Amer. Math. Soc. 348 (1996), 4561-4575. Zbl 0868.16003, MR 1376546 |
| Reference:
|
[4] Golan J.S.: Torsion Theories.Pitman Monographs and Surveys in Pure and Appl. Math. Longman Scientific Publishing, London (1986). Zbl 0657.16017, MR 0880019 |
| Reference:
|
[5] Herbera D., Shamsuddin A.: Modules with semi-local endomorphism rings.Proc. Amer. Math. Soc. 123 (1995), 3593-3600. MR 1277114 |
| Reference:
|
[6] Stenström B.: Rings of Quotients.Springer Berlin (1975). MR 0389953 |
| Reference:
|
[7] Varadarajan K.: Dual Goldie dimension.Comm. Algebra 7 (1979), 565-610. Zbl 0487.16020, MR 0524269 |
| Reference:
|
[8] Facchini A.: Module Theory. Endomorphism rings and direct decompositions in some classes of modules (Lecture Notes).to appear. MR 1634015 |
| . |
