On Gorenstein Projective Dimensions of Unbounded Complexes

Zhongkui Liu , Zhanping Wang

Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (5) : 761 -772.

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Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (5) : 761 -772. DOI: 10.1007/s11401-020-0232-7
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On Gorenstein Projective Dimensions of Unbounded Complexes

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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 R L 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 R L X. It is shown that if R is a Noetherian ring of finite Krull dimension and ϕ: RS is a faithfully flat ring homomorphism, then for any homologically degree-wise finite complex X, there is an equality Gpd R X = Gpd S(S R L X). Similar result is obtained for Ding projective dimension of the S-complex S R L X.

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Gorenstein projective dimension / Ding projective dimension / Faithfully flat ring homomorphism

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Zhongkui Liu, Zhanping Wang. On Gorenstein Projective Dimensions of Unbounded Complexes. Chinese Annals of Mathematics, Series B, 2020, 41(5): 761-772 DOI:10.1007/s11401-020-0232-7

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