范畴X与G(X,Y,Z)的关系  

The relations between the categories X and G(X,Y,Z)

作　　者：孔留贞 KONG Liuzhen(Department of Mathematics and Physics,Nanjing Institute of Technology,211176,Nanjing,Jiangsu,PRC)

机构地区：[1]南京工程学院数理学院,江苏省南京市211167

出　　处：《曲阜师范大学学报（自然科学版）》2023年第4期43-46,共4页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(12271249);南京工程学院人才引进项目(YKJ202038)。

摘　　要：范畴G(X,Y,Z)包含了Gorenstein投射模、Gorenstein内射模、强Gorenstein平坦模和Gorenstein FP-内射模等众多模类,其中范畴X具有举足轻重的作用.这是因为X是G(X,Y,Z)的生成子和余生成子.通过研究维数,证明当模M的G(X,Y,Z)-分解维数有限时,它有特殊的G(X,Y,Z)-预盖;当模M的X-分解维数有限时,M的G(X,Y,Z)-分解维数等于它的X-分解维数.The category G(X,Y,Z)contains Gorenstein projective modules,Gorenstein injective modules,strongly Gorenstein flat modules,Gorenstein FP-injective modules and so on.The category X plays an important role in the category G(X,Y,Z).That is because X is a generator and cogenerator for G(X,Y,Z).By studying relevant dimensions,it is proved that if the G(X,Y,Z)-resolution dimension of M is finite,then it has a special G(X,Y,Z)-precover;if the X-resolution dimension of M is finite,then the G(X,Y,Z)-resolution dimension of M is equal to the X-resolution dimension of M.

关 键 词：G(X Y Z)-模 生成子 预解式 X-分解维数 

分 类 号：O154[理学—数学]