| Title:
|
$\operatorname{Add}(U)$ of a uniserial module (English) |
| Author:
|
Příhoda, Pavel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
391-398 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of $U^{(I)}$ for a uniserial module $U$. It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules. (English) |
| Keyword:
|
serial modules |
| Keyword:
|
direct sum decomposition |
| MSC:
|
16D70 |
| idZBL:
|
Zbl 1106.16006 |
| idMR:
|
MR2281002 |
| . |
| Date available:
|
2009-05-05T16:58:08Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119601 |
| . |
| Reference:
|
[1] Bass H.: Big projective modules are free.Illinois J. Math. 7 (1963), 24-31. Zbl 0115.26003, MR 0143789 |
| Reference:
|
[2] Dung N.V., Facchini A.: Direct sum decompositions of serial modules.J. Pure Appl. Algebra 133 (1998), 93-106. MR 1653699 |
| Reference:
|
[3] Facchini A.: Module Theory; Endomorphism Rings and Direct Sum Decompositions in Some Classes of Modules.Birkhäuser, Basel, 1998. Zbl 0930.16001, MR 1634015 |
| Reference:
|
[4] Příhoda P.: On uniserial modules that are not quasi-small.J. Algebra, to appear. MR 2225779 |
| Reference:
|
[5] Příhoda P.: A version of the weak Krull-Schmidt theorem for infinite families of uniserial modules.Comm. Algebra, to appear. MR 2224888 |
| . |
