| Title:
|
On finitely generated multiplication modules (English) |
| Author:
|
Nekooei, R. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
503-510 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We shall prove that if $M$ is a finitely generated multiplication module and $\mathop {\mathrm Ann}(M)$ is a finitely generated ideal of $R$, then there exists a distributive lattice $\bar{M}$ such that $\mathop {\mathrm Spec}(M)$ with Zariski topology is homeomorphic to $\mathop {\mathrm Spec}(\bar{M})$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$-modules $M$ such that $\mathop {\mathrm Ann}(M)$ is a finitely generated ideal of $R$. (English) |
| Keyword:
|
prime submodules |
| Keyword:
|
multiplication modules |
| Keyword:
|
distributive lattices |
| Keyword:
|
spectral spaces |
| MSC:
|
06B10 |
| MSC:
|
13A15 |
| MSC:
|
13C13 |
| MSC:
|
13C99 |
| idZBL:
|
Zbl 1084.13500 |
| idMR:
|
MR2137157 |
| . |
| Date available:
|
2009-09-24T11:25:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127997 |
| . |
| Reference:
|
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| Reference:
|
[2] T. Duraivel: Topology on spectrum of modules.J. Ramanujan Math. Soc. 9 (1994), 25–34. Zbl 0835.13001, MR 1279099 |
| Reference:
|
[3] M. Hochster: Prime ideal structure in commutative rings.Trans. Amer. Math. Soc. 142 (1969), 43–60. Zbl 0184.29401, MR 0251026, 10.1090/S0002-9947-1969-0251026-X |
| Reference:
|
[4] C. P. Lu: $M$-radicals of submodules in modules.Math. Japon. 34 (1989), 211–219. Zbl 0706.13002, MR 0994584 |
| Reference:
|
[5] C. P. Lu: The Zariski topology on the prime spectrum of a module.Houston J. Math. 25 (1999), 417–432. Zbl 0979.13005, MR 1730888 |
| Reference:
|
[6] R. L. McCasland, M. E. Moore and P. F. Smith: Generators for the semimodule of varieties of a free module.Rocky Mountain J. Math. 29 (1999), 1467–1482. MR 1743380, 10.1216/rmjm/1181070416 |
| Reference:
|
[7] H. Simmons: Reticulated rings.J. Algebra 66 (1980), 169–192. Zbl 0462.13002, MR 0591251, 10.1016/0021-8693(80)90118-0 |
| Reference:
|
[8] P. F. Smith: Some remarks on multiplication modules.Arch. Math. 50 (1998), 223–235. MR 0933916 |
| . |
