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arXiv · 2409.11892

Relative torsionfreeness and Frobenius extensions

Yanhong Bao·Jiafeng Lü·Zhibing Zhao
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Abstract

Let $S/R$ be a Frobenius extension with $_RS_R$ centrally projective over $R$. We show that if $_R\omega$ is a Wakamatsu tilting module then so is $_SS\otimes_R\omega$, and the natural ring homomorphism from the endomorphism ring of $_R\omega$ to the endomorphism ring of $_SS\otimes_R\omega$ is a Frobenius extension in addition that pd$(\omega_T)$ is finite, where $T$ is the endomorphism ring of $_R\omega$. We also obtain that the relative $n$-torsionfreeness of modules is preserved under Frobenius extensions. Furthermore, we give an application, which shows that the generalized G-dimension with respect to a Wakamatsu module is invariant under Frobenius extensions.

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Yanhong Bao, Jiafeng Lü, Zhibing Zhao. 2024-09-18. Relative torsionfreeness and Frobenius extensions. https://arxiv.org/abs/2409.11892

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