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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 2

Characterizing local rings via complete intersection homological dimensions

Fatemeh Mohammadi Aghjeh MASHHAD
Pages
359–364
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $(R,m)$ be a commutative Noetherian local ring.
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Key Findings & Data:It is known that R is Cohen-Macaulay if there exists either a nonzero Cohen-Macaulay R-module of finite projective dimension or a nonzero finitely generated R-module of finite injective dimension.
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Conclusion & Impact:Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Complete intersection homological dimensions · complete intersection ring · CI-regular ring

Abstract

Let $(R,m)$ be a commutative Noetherian local ring. It is known that R is Cohen-Macaulay if there exists either a nonzero Cohen-Macaulay R-module of finite projective dimension or a nonzero finitely generated R-module of finite injective dimension. In this article, we will prove the complete intersection analogues of these facts. Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.

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Cite This Article

MASHHAD, F. M. A. (2022). Characterizing local rings via complete intersection homological dimensions. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 359–364. https://ajindex.com/articles/529772

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