k-torsionfree modules and Frobenius extensions

2023/01/05 by Zhibing Zhao, Zhao, Zhibing · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2301.01903

openalex publication_date 2023/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Base change of (Gorenstein) transpose, k-torsionfree modules, and quasi-faithfully flat extensions

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