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arXiv · 1403.3473

On the Infinitude of Prime Ideals in Dedekind Domains

Jose A. Velez-Marulanda
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Abstract

Let $R$ be an infinite Dedekind domain with at most finitely many units, and let $K$ denote its field of fractions. We prove the following statement. If $L/K$ is a finite Galois extension of fields and $\mathcal{O}$ is the integral closure of $R$ in $L$, then $\mathcal{O}$ contains infinitely many prime ideals. In particular, if $\mathcal{O}$ is further a unique factorization domain, then $\mathcal{O}$ contains infinitely many non-associate prime elements.

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Jose A. Velez-Marulanda. 2014-03-14. On the Infinitude of Prime Ideals in Dedekind Domains. https://arxiv.org/abs/1403.3473

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