Frobenius扩张下的PGF■n-模与Gorenstein■n-平坦模

PGF■n-Modules and Gorenstein■n-Flat Modules under Frobenius Extensions

设R■S是环的Frobenius扩张,M是一个S-模.证明如果R■S是可分Frobenius扩张,则SM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模)当且仅当RM是投射余可解的Gorenstein■n-平坦模(Gorenstein■n-平坦模).

Let R S be a Frobenius extension of rings and M be an S-module.We prove that if R■S is a separable Frobenius extension,then SM is a projectively coresolved Gorenstein■n-flat module(Gorenstein■n-flat module)if and only if RM is a projectively coresolved Gorenstein■n-flat module(Gorenstein■n-flat module).