| Title:
|
Prime and primary submodules of certain modules (English) |
| Author:
|
Amini, A. |
| Author:
|
Amini, B. |
| Author:
|
Sharif, H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
641-648 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we characterize all prime and primary submodules of the free $R$-module $R^{n}$ for a principal ideal domain $R$ and find the minimal primary decomposition of any submodule of $R^{n}$. In the case $n=2$, we also determine the height of prime submodules. (English) |
| Keyword:
|
prime submodules |
| Keyword:
|
primary submodules |
| Keyword:
|
primary decomposition |
| MSC:
|
13C13 |
| MSC:
|
13C99 |
| idZBL:
|
Zbl 1155.13305 |
| idMR:
|
MR2291763 |
| . |
| Date available:
|
2009-09-24T11:36:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128093 |
| . |
| Reference:
|
[1] S. M. George, R. Y. McCasland and P. F. Smith: A principal ideal theorem analogue for modules over commutative rings.Comm. Algebra 22 (1994), 2083–2099. MR 1268545, 10.1080/00927879408824957 |
| Reference:
|
[2] C. P. Lu: Prime submodules of modules.Comment. Math. Univ. St. Paul 33 (1984), 61–69. Zbl 0575.13005, MR 0741378 |
| Reference:
|
[3] H. Matsumura: Commutative Ring Theory.Cambridge University Press, 1986. Zbl 0603.13001, MR 0879273 |
| Reference:
|
[4] R. Y. Sharp: Steps in Commutative Algebra.Cambridge University Press, 1990. Zbl 0703.13001, MR 1070568 |
| Reference:
|
[5] Y. Tiras and A. Harmanci: On prime submodules and primary decomposition.Czechoslovak Math. J. 50 (2000), 83–90. MR 1745462, 10.1023/A:1022441220553 |
| . |
