| Title:
|
On prime submodules and primary decomposition (English) |
| Author:
|
Tiraṣ, Yücel |
| Author:
|
Harmanci, Abdullah |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
83-90 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize prime submodules of $R\times R$ for a principal ideal domain $R$ and investigate the primary decomposition of any submodule into primary submodules of $R\times R.$ (English) |
| Keyword:
|
Prime submodule |
| Keyword:
|
primary submodule |
| Keyword:
|
primary decomposition |
| Keyword:
|
Associated primes |
| MSC:
|
13A15 |
| MSC:
|
13C05 |
| MSC:
|
13C13 |
| MSC:
|
13C99 |
| MSC:
|
13F10 |
| idZBL:
|
Zbl 1036.13010 |
| idMR:
|
MR1745462 |
| . |
| Date available:
|
2009-09-24T10:30:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127551 |
| . |
| Reference:
|
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| Reference:
|
[2] C. P. Lu: Prime submodules of modules.Comm. Math. Univ. Sancti. Pauli 33 (1984), 61–69. Zbl 0575.13005, MR 0741378 |
| Reference:
|
[3] C. P. Lu: $M$-radicals of submodules in modules.Math. Japon. 34 (1989), no. 2, 211–219. Zbl 0706.13002, MR 0994584 |
| Reference:
|
[4] C. P. Lu: $M$-radicals of submodules in modules II.Math. Japon. 35 (1990), no. 5, 991–1001. Zbl 0719.13001, MR 1073902 |
| Reference:
|
[5] S. M. George, R. Y. McCasland and P. F. Smith: A principal ideal theorem analogue for modules over commutative rings.Comm. Algebra 22 (6) (1994), 2083–2099. MR 1268545, 10.1080/00927879408824957 |
| Reference:
|
[6] R. Y. McCasland and M. E. Moore: On radicals of submodules of finitely generated modules.Canad. Math. Bull. 29 (1) (1986). MR 0824879, 10.4153/CMB-1986-006-7 |
| Reference:
|
[7] R. Y. McCasland and P. F. Smith: Prime submodules of Noetherian modules.Rocky Mountain J. Math. 23 (1993), no. 3. MR 1245463, 10.1216/rmjm/1181072540 |
| Reference:
|
[8] H. Matsumura: Commutative Ring Theory.Cambridge University Press, 1980. MR 0879273 |
| Reference:
|
[9] R. Y. Sharp: Steps in Commutative Algebra.Cambridge University Press, 1990. Zbl 0703.13001, MR 1070568 |
| . |
