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Bibliographic Details
Main Author: Bartels, Richard F.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.11144
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author Bartels, Richard F.
author_facet Bartels, Richard F.
contents For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences and localizing at prime ideals. We then give conditions for when ideals in a one-dimensional Cohen-Macaulay local ring are Elias and Burch, and use these conditions to study the relationship between Elias, Burch, and Ulrich ideals.
format Preprint
id arxiv_https___arxiv_org_abs_2410_11144
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Some properties of ideals in Cohen-Macaulay local rings
Bartels, Richard F.
Commutative Algebra
For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences and localizing at prime ideals. We then give conditions for when ideals in a one-dimensional Cohen-Macaulay local ring are Elias and Burch, and use these conditions to study the relationship between Elias, Burch, and Ulrich ideals.
title Some properties of ideals in Cohen-Macaulay local rings
topic Commutative Algebra
url https://arxiv.org/abs/2410.11144