| Autor: |
POURMORTAZAVI, S. S., KEYVANI, S. |
| Předmět: |
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| Zdroj: |
Journal of Algebra & Related Topics; Jun2023, Vol. 11 Issue 1, p49-53, 5p |
| Abstrakt: |
Let R be a commutative ring with identity, and let M be an R-module. The Cohen's theorem is the classic result that a ring is Noetherian if and only if its prime ideals are finitely generated. Parkash and Kour obtained a new version of Cohen's theorem for modules, which states that a finitely generated R-module M is Noetherian if and only if for every prime ideal p of R with Ann(M) ⊆ p, there exists a finitely generated submodule N of M such that pM ⊆ N ⊆ M(p), where M(p) = {x ∈ M|sx ∈ pM for some s ∈ R\p. In this paper, we prove this result for some classes of modules. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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