On Gorenstein Projective Dimensions of Unbounded Complexes
Zhongkui Liu , Zhanping Wang
Chinese Annals of Mathematics, Series B ›› 2020, Vol. 41 ›› Issue (5) : 761 -772.
On Gorenstein Projective Dimensions of Unbounded Complexes
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: R → S 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.
Gorenstein projective dimension / Ding projective dimension / Faithfully flat ring homomorphism
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