斜群环上的Gorenstein AC平坦模  

Gorenstein AC Flat Modules of Skew Group Rings

作　　者：秦岭 Qin Ling(College of Mathematical Science,Chongqing Normal University,Shapingba401331,Chongqing)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《商洛学院学报》2024年第4期29-33,共5页Journal of Shangluo University

基　　金：国家自然科学基金项目(11871125);重庆市教委项目(KJQN201800509)。

摘　　要：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.

关 键 词：斜群环 Gorenstein AC-平坦模 弱Gorenstein AC整体维数 可分扩张 

分 类 号：O154.2[理学—数学]