G_C-projectivity and injectivity under Frobenius extensions

Abstract

In this article, we prove that Gorenstein projectivity and injectivity with respect to a semidualizing module are preserved under Frobenius extensions. Furthermore, we obtain that the G_C-projective and injective dimensions of modules are invariant under Frobenius extensions. As corollaries, we get some Gorenstein homological dimensions are preserved under Frobenius extensions, which show that Gorenstein homological dimensions have better invariant properties than the classical homological dimensions under Frobenius extensions.

Keywords:

• Frobenius extensions
• G_C-projective dimensions
• G_C-projective modules
• semidualizing modules

2020 Mathematics Subject Classification:

• 13B02
• 16D80
• 16E10
• 16G50

Additional information

Funding

This work was partially supported by National Natural Science Foundation of China (No. 11871071) and Project of University Natural Science Research of Anhui Province (No. KJ2019A0007). The author thanks the referees for your comments.