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arXiv · 2308.01357

Gluing Associated Prime Ideals of Small Height

S. Loepp·Liz Ostermeyer
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Abstract

Let $B$ be a local (Noetherian) ring and suppose that $B$ has $n$ associated prime ideals where $n \geq 2$. We identify sufficient conditions for there to exist a local (Noetherian) subring $S$ of $B$ such that $S$ and $B$ have the same completion and $S$ has exactly $n - 1$ associated prime ideals. We include applications and consequences of this result.

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S. Loepp, Liz Ostermeyer. 2023-08-02. Gluing Associated Prime Ideals of Small Height. https://arxiv.org/abs/2308.01357

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