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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
As applications, we obtain new characterizations of Gorenstein and regular local rings.
📌 3 Key Takeaways
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Objective & Hypothesis:Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module with finite projective dimension and N an arbitrary R-module with finite Cohen-Macaulay injective dimension.
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Key Findings & Data:In this paper, we show that the generalized local cohomology Hi a(M, N) is zero for every i larger than the Cohen-Macaulay injective dimension of N.
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Conclusion & Impact:As applications, we obtain new characterizations of Gorenstein and regular local rings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cohen-Macaulay injective dimension · dualizing module · generalized local cohomology
Abstract
Let a be an ideal of a commutative Noetherian ring R, M a finitely generated R-module with finite projective dimension and N an arbitrary R-module with finite Cohen-Macaulay injective dimension. In this paper, we show that the generalized local cohomology Hi a(M, N) is zero for every i larger than the Cohen-Macaulay injective dimension of N. As applications, we obtain new characterizations of Gorenstein and regular local rings.
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Cite This Article
TANG, X. (2022). Some applications of Cohen-Macaulay injective dimension. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 5, 777–785. https://ajindex.com/articles/530344