摘要
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(Cohen-Macaulay)-finite(resp.CM-free)if and only if so is the base algebra.Furthermore,we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.
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(Cohen-Macaulay)-finite(resp.CM-free) if and only if so is the base algebra. Furthermore, we prove that the representation dimension of Artin algebras is invariant under separable Frobenius extensions.
基金
supported by National Natural Science Foundation of China(Grant No.11571329)
the Natural Science Foundation of Anhui Province(Grant No.1708085MA01)
