Relative torsionfreeness and Frobenius extensions

Yanhong Bao; Jiafeng LÃ¼; Zhibing Zhao

paper

Relative torsionfreeness and Frobenius extensions

arXiv:2409.11892

Abstract

Let $S / R$ be a Frobenius extension with $_{R} S_{R}$ centrally projective over $R$ . We show that if $_{R} I ¨ $ is a Wakamatsu tilting module then so is $_{S} S \otimes_{R} I ¨ $ , and the natural ring homomorphism from the endomorphism ring of $_{R} I ¨ $ to the endomorphism ring of $_{S} S \otimes_{R} I ¨ $ is a Frobenius extension in addition that pd $(I ¨ _{T})$ is finite, where $T$ is the endomorphism ring of $_{R} I ¨ $ . 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.

arXiv admin note: text overlap with arXiv:2301.01903