Gorenstein homological invariant properties under Frobenius extensions

2017/12/25 by Zhibing, Zhao · 1 citation
#13B02 #16E10 #16G10 #16G50 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1712.09111

Abstract

We prove that for a Frobenius extension, a module over the extension ring is Gorenstein projective if and only if its underlying module over the base ring is Gorenstein projective. For a separable Frobenius extension between Artin algebras, we obtain that the extension algebra is CM-finite (resp. CM-free) if and only if so is the base algebra. Furthermore, we prove that the reprensentation dimension of Artin algebras is invariant under separable Forbenius extensions.

Cited by

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

Related

• Gorenstein projective modules and Frobenius extensions
• Frobenius functors and Gorenstein projective precovers
• Gorenstein Homological Algebra of Artin Algebras
• Gorenstein dimensions in trivial ring extensions
• Invariants and Gorenstein projective modules