On Cohen’s theorem for modules

Anand Parkash () and Surjeet Kour ()
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Anand Parkash: Indian Institute of Technology Indore
Surjeet Kour: Indian Institute of Technology Delhi

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 3, 869-871

Abstract: 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 $$Ann(M) \subseteq P$$ A n n ( M ) ⊆ P , there exists a finitely generated submodule $$N_P$$ N P of M such that $$PM \subseteq N_P \subseteq M(P)$$ P M ⊆ N P ⊆ M ( P ) .

Keywords: Finitely generated submodules; Noetherian modules; 13C13; 13C99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00101-z

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