| Title:
|
Projective modules and prime submodules (English) |
| Author:
|
Alkan, Mustafa |
| Author:
|
Tiraş, Yücel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
601-611 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we use Zorn’s Lemma, multiplicatively closed subsets and saturated closed subsets for the following two topics: (i) The existence of prime submodules in some cases, (ii) The proof that submodules with a certain property satisfy the radical formula. We also give a partial characterization of a submodule of a projective module which satisfies the prime property. (English) |
| Keyword:
|
prime submodule |
| Keyword:
|
primary submodule |
| Keyword:
|
${\scr S}$-closed subsets |
| Keyword:
|
the radical formula |
| MSC:
|
13A10 |
| MSC:
|
13A99 |
| MSC:
|
13C10 |
| MSC:
|
13C13 |
| idZBL:
|
Zbl 1155.13300 |
| idMR:
|
MR2291760 |
| . |
| Date available:
|
2009-09-24T11:36:00Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128090 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] C. U. Jensen: A remark on flat and projective modules.Canad. J. Math. 18 (1966), 943–949. Zbl 0144.02302, MR 0199226, 10.4153/CJM-1966-093-7 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] R. L. McCasland, P. F. Smith: Prime submodules of Noetherian modules.Rocky Mountain J. Math 23 (1993), 1041–1062. MR 1245463, 10.1216/rmjm/1181072540 |
| Reference:
|
[9] D. Pusat-Yilmaz, P. F. Smith: Modules which satisfy the radical formula.Acta. Math. Hungar. 1–2 (2002), 155–167. MR 1906216, 10.1023/A:1015624503160 |
| Reference:
|
[10] P. F. Smith: Primary modules over commutative rings.Glasgow Math. J. 43 (2001), 103–111. Zbl 0979.13003, MR 1825725, 10.1017/S0017089501010084 |
| Reference:
|
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| . |
