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arXiv · 1708.09008

Assassins and torsion functors

Fred Rohrer
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Abstract

Let $R$ be a ring, let $\mathfrak{a}\subseteq R$ be an ideal, and let $M$ be an $R$-module. Let $\Gamma_{\mathfrak{a}}$ denote the $\mathfrak{a}$-torsion functor. Conditions are given for the (weakly) associated primes of $\Gamma_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ containing $\mathfrak{a}$, and for the (weakly) associated primes of $M/\Gamma_{\mathfrak{a}}(M)$ to be the (weakly) associated primes of $M$ not containing $\mathfrak{a}$.

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Fred Rohrer. 2017-08-29. Assassins and torsion functors. https://doi.org/10.1007/s40306-017-0233-0

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