On finitely generated multiplication modules
Czechoslovak Mathematical Journal (2005)
- Volume: 55, Issue: 2, page 503-510
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topNekooei, R.. "On finitely generated multiplication modules." Czechoslovak Mathematical Journal 55.2 (2005): 503-510. <http://eudml.org/doc/30964>.
@article{Nekooei2005,
abstract = {We shall prove that if $M$ is a finitely generated multiplication module and $\mathop \{\mathrm \{A\}nn\}(M)$ is a finitely generated ideal of $R$, then there exists a distributive lattice $\bar\{M\}$ such that $\mathop \{\mathrm \{S\}pec\}(M)$ with Zariski topology is homeomorphic to $\mathop \{\mathrm \{S\}pec\}(\bar\{M\})$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$-modules $M$ such that $\mathop \{\mathrm \{A\}nn\}(M)$ is a finitely generated ideal of $R$.},
author = {Nekooei, R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {prime submodules; multiplication modules; distributive lattices; spectral spaces; prime submodules; multiplication modules; spectrum of distributive lattice},
language = {eng},
number = {2},
pages = {503-510},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On finitely generated multiplication modules},
url = {http://eudml.org/doc/30964},
volume = {55},
year = {2005},
}
TY - JOUR
AU - Nekooei, R.
TI - On finitely generated multiplication modules
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 2
SP - 503
EP - 510
AB - We shall prove that if $M$ is a finitely generated multiplication module and $\mathop {\mathrm {A}nn}(M)$ is a finitely generated ideal of $R$, then there exists a distributive lattice $\bar{M}$ such that $\mathop {\mathrm {S}pec}(M)$ with Zariski topology is homeomorphic to $\mathop {\mathrm {S}pec}(\bar{M})$ to Stone topology. Finally we shall give a characterization of finitely generated multiplication $R$-modules $M$ such that $\mathop {\mathrm {A}nn}(M)$ is a finitely generated ideal of $R$.
LA - eng
KW - prime submodules; multiplication modules; distributive lattices; spectral spaces; prime submodules; multiplication modules; spectrum of distributive lattice
UR - http://eudml.org/doc/30964
ER -
References
top- Distributive Lattices, Univ. of Missouri Press, Missouri, 1974. (1974) MR0373985
- Topology on spectrum of modules, J. Ramanujan Math. Soc. 9 (1994), 25–34. (1994) Zbl0835.13001MR1279099
- 10.1090/S0002-9947-1969-0251026-X, Trans. Amer. Math. Soc. 142 (1969), 43–60. (1969) Zbl0184.29401MR0251026DOI10.1090/S0002-9947-1969-0251026-X
- -radicals of submodules in modules, Math. Japon. 34 (1989), 211–219. (1989) Zbl0706.13002MR0994584
- The Zariski topology on the prime spectrum of a module, Houston J. Math. 25 (1999), 417–432. (1999) Zbl0979.13005MR1730888
- 10.1216/rmjm/1181070416, Rocky Mountain J. Math. 29 (1999), 1467–1482. (1999) MR1743380DOI10.1216/rmjm/1181070416
- 10.1016/0021-8693(80)90118-0, J. Algebra 66 (1980), 169–192. (1980) Zbl0462.13002MR0591251DOI10.1016/0021-8693(80)90118-0
- Some remarks on multiplication modules, Arch. Math. 50 (1998), 223–235. (1998) MR0933916
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.