On Gorenstein Projective Dimensions of Unbounded Complexes |
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Authors: | Zhongkui LIU Zhanping WANG |
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Institution: | Department of Mathematics, Northwest Normal University, Lanzhou 730070, China.; Correspoinding author. Department of Mathematics, Northwest Normal University, Lanzhou 730070,China. |
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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 ?LR
X 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 ?LR
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 ?LR
X). Similar result is obtained for Ding projective dimension of the S-complex S ?LR
X. |
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Keywords: | Gorenstein projective dimension Ding projective dimension Faithfully flat ring homomorphism |
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