“…It is well-known that many homological properties are preserved under Frobenius extensions (see [7,8,13,22,24]). So there is a natural question: are the k-torsionfreeness of modules preserved under Frobenius extensions?…”
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 R is a quasi k-Gorenstein ring if and only if so is S.
“…It is well-known that many homological properties are preserved under Frobenius extensions (see [7,8,13,22,24]). So there is a natural question: are the k-torsionfreeness of modules preserved under Frobenius extensions?…”
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 R is a quasi k-Gorenstein ring if and only if so is S.
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