Transfer of Gorenstein Dimensions of Unbounded Complexes Along Ring Homomorphisms
Transfer of Gorenstein Dimensions of Unbounded Complexes Along Ring Homomorphisms
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DOI：
10.1080/00927872.2013.783039
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发表时间：
2014-04
影响因子：
0.7
通讯作者：
Liu Zhongkui;R. Wei
中科院分区：
文献类型：
--
作者：
Liu Zhongkui;R. Wei
Let R → S be a ring homomorphism. We consider the relationships of the Gorenstein dimensions of an R-complex X (possibly unbounded) with those of the S-complexes RHom R (S, X) and . More generally, the Gorenstein injective dimension of RHom R (U, X) is considered where U is an S-complex with finite projective dimension. As an application, it is shown that if R is a local noetherian ring, then a complex X of R-modules has finite Gorenstein projective dimension if and only if it has finite Gorenstein flat dimension if and only if belongs to the Auslander category . This gives a resolution-free characterizations of complexes for which their Gorenstein projective dimensions are finite.
