摘要
We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extension is either left-Gorenstein or separable(e.g., the integral group ring extension ZZG).Moreover, for the Frobenius extension RA = R[x]/(x^2), we show that: a graded A-module is Gorenstein projective in GrMod(A), if and only if its ungraded A-module is Gorenstein projective, if and only if its underlying R-module is Gorenstein projective. It immediately follows that an R-complex is Gorenstein projective if and only if all its items are Gorenstein projective R-modules.
We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein projective,then its underlying module over the base ring is Gorenstein projective; the converse holds if the frobenius extension is either left-Gorenstein or separable（e.g., the integral group ring extension Z■ZG）.Moreover, for the Frobenius extension R■A = R[x]/（x2）, we show that： a graded A-module is Gorenstein projective in GrMod（A）, if and only if its ungraded A-module is Gorenstein projective, if and only if its underlying R-module is Gorenstein projective. It immediately follows that an R-complex is Gorenstein projective if and only if all its items are Gorenstein projective R-modules.
基金
supported by National Natural Science Foundation of China(Grant No.11401476)
China Postdoctoral Science Foundation(Grant No.2016M591592)
