摘要
设R是一个交换诺特环且S是R的乘法闭子集.如果G是一个有限生成的(半)Gorenstein投射右R-模,则S^(-1)G是一个有限生成的(半)Gorenstein投射右S^(-1)R-模.如果S^(-1)R是忠实平坦的,则R满足Gorenstein投射猜想可推出S^(-1)R满足Gorenstein投射猪想.特别地、In如果R是交换阿廷环且E一个有限生成的Gorenstein内射右R-模,则S^(-1)E是一个有限生成的Gorenstein内射S^(-1)R-模.
Let R be a commutative noetherian ring R and S■R a multiplicative set.If G is a nitely generated(semi-)Gorenstein projective R-module,then S^(-1)G is a nitely generated(semi-)Gorenstein projective S^(-1)R-module.In case S^(-1)R is faith-fully at,then S^(-1)R satis es Gorenstein projective conjecture if R satis es Goren-stein projective conjecture.In addition,if R is artinian and E is a nitely generated Gorenstein injective R-module,then S^(-1)E is a nitely generated Gorenstein injective S^(-1)R-module.
作者
张孝金
庄颖
Zhang Xiaojin;Zhuang Ying(School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116;School of Mathematics and Statistics,NUIST,Nanjing 210044;Suzhou Jinchang Middle School,Suzhou 215600)
出处
《南京大学学报（数学半年刊）》
2021年第2期198-213,共16页
Journal of Nanjing University(Mathematical Biquarterly)
基金
Supported by NSFC(Nos.11671174,12171207)
the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions and the Starting Fund of Jiangsu Normal University.
