Abstract
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 \(Ann(M) \subseteq P\), there exists a finitely generated submodule \(N_P\) of M such that \(PM \subseteq N_P \subseteq M(P)\).
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Communicated by Jugal K Verma.
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Parkash, A., Kour, S. On Cohen’s theorem for modules. Indian J Pure Appl Math 52, 869–871 (2021). https://doi.org/10.1007/s13226-021-00101-z
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DOI: https://doi.org/10.1007/s13226-021-00101-z