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arXiv · 2410.11144

Some properties of ideals in Cohen-Macaulay local rings

Richard F. Bartels
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Abstract

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.

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Richard F. Bartels. 2024-10-14. Some properties of ideals in Cohen-Macaulay local rings. https://arxiv.org/abs/2410.11144

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