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Post Closed as "Not suitable for this site" by Venkataramana, Andreas Blass, Karl Schwede, Stefan Kohl♦, S. Carnahan♦
texified the title; punctuation
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edit approved Sep 26, 2014 at 17:09
GNiklasch
edit approved Sep 26, 2014 at 17:09
GNiklasch
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Units of an extension of \mathbb$\mathbb{Z}$

Let $P(x)\in\mathbb{Z}[x]$ be monic and irreducible over $\mathbb{Q}[x]$, and let $\theta$ be a root of $P(x)$. Let $K = \{a + b\theta\} \subset \mathbb{Z}[\theta]$$K = \{a + b\theta\} \subseteq \mathbb{Z}[\theta]$. When is it the case that there are infinitely many $\alpha\in K$ s.t. $\text{Nm}(\alpha) = 1$?

Units of an extension of \mathbb{Z}

Let $P(x)\in\mathbb{Z}[x]$ be monic and irreducible over $\mathbb{Q}[x]$, and let $\theta$ be a root of $P(x)$ Let $K = \{a + b\theta\} \subset \mathbb{Z}[\theta]$. When is it the case that there are infinitely many $\alpha\in K$ s.t. $\text{Nm}(\alpha) = 1$?

Units of an extension of $\mathbb{Z}$

Let $P(x)\in\mathbb{Z}[x]$ be monic and irreducible over $\mathbb{Q}[x]$, and let $\theta$ be a root of $P(x)$. Let $K = \{a + b\theta\} \subseteq \mathbb{Z}[\theta]$. When is it the case that there are infinitely many $\alpha\in K$ s.t. $\text{Nm}(\alpha) = 1$?

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Mayank Pandey
Mayank Pandey
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Units of an extension of \mathbb{Z}

Let $P(x)\in\mathbb{Z}[x]$ be monic and irreducible over $\mathbb{Q}[x]$, and let $\theta$ be a root of $P(x)$ Let $K = \{a + b\theta\} \subset \mathbb{Z}[\theta]$. When is it the case that there are infinitely many $\alpha\in K$ s.t. $\text{Nm}(\alpha) = 1$?