斜群环上的Gorenstein AC平坦模

Gorenstein AC Flat Modules of Skew Group Rings

为研究在可分扩张下Gorenstein AC-平坦模在斜群环中的同调性质。在R^(σ)G→R^(σ)H是斜群环的可分扩张条件下,证明了限制函子和诱导函子保持模的FP_(∞)-内射、level和Gorenstein AC-平坦等同调性质。若Gorenstein AC-平坦模类关于扩张封闭,斜群环R^(σ)G和R^(σ)H具有相等的弱Gorenstein AC整体维数。

To investigate the homomorphism of Gorenstein AC-flat modulus in skew group rings under separable extension,it is proved that the restriction functor and induced functor keep the homomorphism of FP∞-injective,level and Gorenstein AC-flat modulus under the condition that R^(σ)G→R^(σ)H is the separable extension of the skew group rings;if the Gorenstein AC-flat modulus class is closed with respect to the extension,the skew group rings R^(σ)G and R^(σ)H have equal weak Gorenstein AC global dimensions.