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Yapay Zeka Hızlı Bakış & Çıkarımlar
AI Insight⚡ TL;DR(1 Cümlede Hızlı Çıkarım)
As applications, we obtain new characterizations of Gorenstein and regular local rings.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:As applications, we obtain new characterizations of Gorenstein and regular local rings.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.
Anahtar kelimeler
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Bu Makaleye Atıf Yap
Tang, X. (2014). Some applications of Cohen-Macaulay injective dimension. Hacettepe Journal of Mathematics and Statistics, Volume: 43 Issue: 5. https://ajindex.com/articles/1403370