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Results tagged with torsion
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user 11025
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Torsion submodules of non-noetherian modules
The $\mathfrak{a}$-torsion submodule of $M$ is defined as $$\Gamma_{\mathfrak{a}}(M)=\{x\in M\mid\mathfrak{a}\subseteq\sqrt{(0:_Rx)}\}.$$ If $R$ or $M$ is noetherian, then this submodule has lots of nice …
- 6,700
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Torsion functors and weak assassins
Let $R$ be a commutative ring, and let $\mathfrak{a}\subseteq R$ be an ideal. For an $R$-module $M$, we set $\Gamma_{\mathfrak{a}}(M)=\{x\in M\mid\exists n\in\mathbb{N}:\mathfrak{a}^nx=0\}$, and we de …
- 6,700