✨
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
🎯
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.
📊
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.
💡
Sonuç & Katkı:As applications, we obtain new characterizations of Gorenstein and regular local rings.
🔬Tür:Araştırma Makalesi
📍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
🔖
Bu Makaleye Atıf Yap
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