# Tagged Questions

**2**

votes

**1**answer

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### Is there a Dirichlet Unitary Unit Theorem?

Dirichlet's unit theorem computes the group of units of the algebraic numbers of a number field. There are a few generalisations for orders available.
Assume the order has an involution. For example, ...

**6**

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**2**answers

479 views

### What is the set of possible values of the degree of the sum of two algebraic numbers with fixed degrees?

This question is related to Degree of sum of algebraic numbers and algebraic numbers of degree 3 and 6, whose sum has degree 12.
In this last question I asked a very special case of the following ...

**5**

votes

**3**answers

545 views

### Transformations of integer polynomials under combinations of their roots

I'm wondering whether the following ideas/questions give rise to an existing body of research. (Accordingly: please suggest appropriate changes to the tags!)
Preamble
We consider polynomials ...

**1**

vote

**2**answers

291 views

### Infinite collection of elements of a number field with very similar annihilating polynomials

Hello all, let $n$ be an integer $\geq 2$ and let $\alpha$ be an algebraic number
of degree $n$. Let $R$ be the ring of algebraic integers in ${\mathbb Q}(\alpha)$, and
let $B$ be the subset of $R$ ...

**14**

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**6**answers

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### Solving polynomial equations when you know in which number field the solutions live

Suppose I have a bunch of polynomial equations with coefficients in a number field, and suppose further that I'm guaranteed a priori that they have a solution in that number field. Can I leverage ...