A Generalization of a Theorem of Bass
2006; Taylor & Francis; Volume: 35; Issue: 1 Linguagem: Inglês
10.1080/00927870601041672
ISSN1532-4125
Autores Tópico(s)Algebraic Geometry and Number Theory
ResumoAbstract Let (R, 𝔪) be a commutative Noetherian local ring. In this paper we prove that if R admits a finite module of finite Gorenstein injective dimension and maximal Krull dimension then R is Cohen–Macaulay. This generalizes a theorem of Bass and improves a recent result of Takahashi where the ring is assumed to have a dualizing complex. Key Words: Cohen–Macaulay ringGorenstein injective dimensionLocal cohomology module2000 Mathematics Subject Classification: 13C1113H1013D45 ACKNOWLEDGMENTS This article was prepared during the author's visit to the Institut des Hautes Études Scientifiques (IHES). He would like to thank the authorities of IHES for their hospitality during his stay there. He also thanks his colleague R. Zaare-Nahandi for reading the final manuscript. The author was supported in part by a grant from University of Tehran (No. 6103023/1/03). Notes Communicated by I. Swanson.
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