Abstract
Let \(R\rightarrow S\) be a local ring homomorphism and N a finitely generated S-module. We prove that if the Gorenstein injective dimension of N over R is finite, then it equals the depth of R.
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We thank the anonymous referee for suggestions and comments that helped us improve the exposition.
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L.W.C. was partly supported by Simons Foundation collaboration Grant 428308; D.W. was partly supported by NSF of China Grants 11761047 and 11861043. The paper was written during D.W.’s year-long visit to Texas Tech University; the hospitality of the TTU Department of Mathematics and Statistics is acknowledged with gratitude.
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Christensen, L.W., Wu, D. A Bass equality for Gorenstein injective dimension of modules finite over homomorphisms. Arch. Math. 113, 459–467 (2019). https://doi.org/10.1007/s00013-019-01346-1
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DOI: https://doi.org/10.1007/s00013-019-01346-1