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| On Gorenstein Projective Dimensions of Unbounded Complexes |
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Citation： |
Zhongkui LIU,Zhanping WANG.On Gorenstein Projective Dimensions of Unbounded Complexes[J].Chinese Annals of Mathematics B,2020,41(5):761~772 |
| Page view： 561
Net amount： 367 |
Authors： |
Zhongkui LIU; Zhanping WANG |
Foundation： |
Mathematics Research Center of Sichuan Normal University and V. C. & V. R. Key Lab of Sichuan Province, by Science and Technology Research Program of Chongqing Education Commission of China (No. KJ1600324) and Natural Science Foundation of Chongqing, China (No. cstc2018jcyjAX0465). |
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| Abstract： |
Let R → S be a ring homomorphism and X be a complex of R-modules. Then the complex of S-modules S?LRX 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 ?LRX. It is shown that if R is a Noetherian ring of finite Krull dimension and φ : R → S is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality GpdRX = GpdS(S ?LRX). Similar result is obtained for Ding projective dimension of the S-complex S ?LRX. |
Keywords： |
Gorenstein projective dimension, Ding projective dimension, Faithfully flat ring homomorphism |
Classification： |
13D05, 13D25 |
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