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$k$-torsionfree modules and Frobenius extensions (2301.01903v2)
Published 5 Jan 2023 in math.RT
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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