@article{Fu2022, 
author = {Dongxing Fu and Xiaowei Xu and Zhibing Zhao},
title = {Generalized tilting modules and Frobenius extensions},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {9},
pages = {3337-3350},
keywords = {generalized tilting modules, Frobenius extensions, separable extensions, ⊥ω-dimensions, ⊥ω-Gorenstein projective modules},
url = {https://www.sciopen.com/article/10.3934/era.2022169},
doi = {10.3934/era.2022169},
abstract = {Let  A/S be a ring extension with  S commutative. We prove that  ω⊗SAA is a generalized tilting module if  ωS is a generalized tilting module. In this case, we obtain that  ⊥ω-resol.dim S(M) and  ⊥(ω⊗SA)-resol.dim A(M) are identical for any  A-module  M. As an application, we show that  S satisfies gorenstein symmetric Conjecture if and only if so does  A. Furthermore, we introduce the concept of  ⊥ω-Gorenstein projective modules, and we obtain that the relative Gorenstein projectivity is invariant under Frobenius extensions.}
}