On Cohen’s theorem for modules
In this paper, we prove that if R is a commutative ring with unity and M is a finitely generated R -module, then M is Noetherian if and only if for every prime ideal P of R with A n n ( M ) ⊆ P , there exists a finitely generated submodule N P of M such that P M ⊆ N P ⊆ M ( P ) .
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| Veröffentlicht in: | Indian journal of pure and applied mathematics 2021-09, Vol.52 (3), p.869-871 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we prove that if
R
is a commutative ring with unity and
M
is a finitely generated
R
-module, then
M
is Noetherian if and only if for every prime ideal
P
of
R
with
A
n
n
(
M
)
⊆
P
, there exists a finitely generated submodule
N
P
of
M
such that
P
M
⊆
N
P
⊆
M
(
P
)
. |
|---|---|
| ISSN: | 0019-5588 0975-7465 |
| DOI: | 10.1007/s13226-021-00101-z |