局部化与Gorenstein投射和Gorenstein内射模  

LOCALIZATION OF GORENSTEIN PROJECTIVE AND INJECTIVE MODULES

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)

机构地区：[1]江苏师范大学数学与统计学院,徐州21116 [2]南京信息工程大学数学与统计学院,南京210044 [3]苏州金闾实验中学,苏州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.

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.

关 键 词：局部化 Gorenstein投射 Gorenstein内射 交换诺特环 

分 类 号：O154.2[理学—数学]