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

Characterizing local rings via complete intersection homological dimensions

Fatemeh Mohammadi Aghjeh MASHHAD
Sayfa
359–364
Yayın Tarihi
2022-10-18
DOI
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Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $(R,m)$ be a commutative Noetherian local ring.
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Temel Bulgular & Veri: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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Sonuç & Katkı:Also, by using complete intersection homological dimensions, we will characterize local rings which are either regular, complete intersection or Gorenstein.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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