$k$-torsionfree modules and Frobenius extensions

Zhibing Zhao

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arXiv · 2301.01903

$k$-torsionfree modules and Frobenius extensions

Zhibing Zhao

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Abstract

Let $R/S$ be a Frobenius extension and $k$ be a positive integer. We prove that an $R$-module is $k$-torsionfree if and only if so is its underlying $S$-module. As an application, we obtain that if $S$ is a quasi $k$-Gorenstein ring then so is $R$, but the converse does not hold in general.

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Zhibing Zhao. 2023-01-05. $k$-torsionfree modules and Frobenius extensions. https://arxiv.org/abs/2301.01903

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