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articleNo Access
A Cohen-type theorem for $w$ $w$ -Artinian modules
- Dechuan Zhou,
- Hwankoo Kim, and
- Kui Hu
Journal of Algebra and Its Applications02 Jun 2020
Preview Abstract
Let $R$ $R$ be a commutative ring with identity. In this paper, a Cohen-type theorem for $w$ $w$ -Artinian modules is given, i.e. a $w$ $w$ -cofinitely generated $R$ $R$ -module $M$ $M$ is $w$ $w$ -Artinian if and only if ${(M / {ann}_{M} (P))}_{w}$ ${(M / {ann}_{M} (P))}_{w}$ is $w$ $w$ -cofinitely generated for every prime $w$ $w$ -ideal $P$ $P$ of $R$ $R$ . As a by-product of the proof, we also obtain a detailed representation of elements of a $w$ $w$ -module and the $w$ $w$ -theoretic version of the Chinese remainder theorem for both modules and rings.

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