A Homological Characterization and Unique Factorization of Property Regular Local Rings

Patra, Trishita (2023) A Homological Characterization and Unique Factorization of Property Regular Local Rings. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (Ms dissertation of Trishita Patra (18MS188)) Thesis_18MS188.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

The two main theorems of this thesis are Serre's characterization of regular local rings, which says that a Noetherian local ring is regular if and only if its global dimension is finite and in that case global dimension and Krull dimension are equal; the second theorem says that any regular local ring is a unique factorization domain. We study notion of dimension from both homological algebraic and ring theoretic perspective, and properties of a regular local ring. We finally prove the theorems using results from commutative algebra and homological algebra.

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