On Gorenstein Projective Dimensions of Unbounded Complexes  

作　　者：Zhongkui LIU Zhanping WANG 

机构地区：[1]Department of Mathematics,Northwest Normal University,Lanzhou 730070,China [2]Correspoinding author.Department of Mathematics,Northwest Normal University,Lanzhou 730070,China

出　　处：《Chinese Annals of Mathematics,Series B》2020年第5期761-772,共12页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11261050,11561061).

摘　　要：Let R→S be a ring homomorphism and X be a complex of R-modules.Then the complex of S-modules S L RX in the derived category D(S)is constructed in the natural way.This paper is devoted to dealing with the relationships of the Gorenstein projective dimension of an R-complex X(possibly unbounded)with those of the S-complex S■R^L X.It is shown that if R is a Noetherian ring of finite Krull dimension and:R→S is a faithfully flat ring homomorphism,then for any homologically degree-wise finite complex X,there is an equality GpdRX=GpdS(S■R^LX).Similar result is obtained for Ding projective dimension of the S-complex S■R^L X.

关 键 词：Gorenstein projective dimension Ding projective dimension Faithfully flat ring homomorphism 

分 类 号：O153.5[理学—数学]