# Tagged Questions

Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].

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### Isomorphism problem for finite dimensional central division algebras over a function field in two indeterminates.

Let K be the fraction field of C[x,y] where C denotes the complex numbers. Suppose D and E are two central division algebras over K of degree n, i.e. dim(D)=dim(E)=n^2. Is there any natural criterium ...
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### Behaviour of Primes under Regular Coefficient Extensions

Let $K\hookrightarrow K'$ be a regular extension of fields, and $K[x_{1},\cdots,x_{n}]\hookrightarrow K'[x_{1},\cdots,x_{n}]$ the corresponding ring extension. Does every prime ideal of the first ring ...
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### Is Every field Extension of an Ultrafield an Ultrafield?

Let $K=lim(K_{i})$ be an ultrafield (over a non-principal ultrafilter), and let $K\hookrightarrow K'$ be a field extension of $K$. When the field $K'$ is finite over $K$ it is also an ultrafield by ...
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### Valuations and separable extensions

Let $R$ be a valuation ring containing a field $k$, with residue field $F$ and quotient field $K$. Assume $F/k$ is separable. Is $K/k$ separable? I have convinced myself that (for a positive answer) ...
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### Weakly initial sets - examples and nonexamples

A weakly initial set in a category C is a set of objects I of C such that every object a of C has at least one arrow from an object contained in I. The question is then, does Fields have a weakly ...
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### FFTs over finite fields?

I'm trying to understand how to compute a fast Fourier transform over a finite field. This question arose in the analysis of some BCH codes. Consider the finite field $F$ with $2^n$ elements. It is ...
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### An alternative description of K^*/Nm(L^*)

Is there a nice explicit description for the group $K^*/Nm_{L/K}(L^*)$ for a finite field extension $L/K$? What if for example, $L$ is obtained from $K$ by ajoining an n-th root of some \$\alpha \in ...
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### Is there a field which is the union of finitely many proper subfields?

Is there a field which is the union of finitely many proper subfields?
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### What are examples of ordered fields that do not have the Archimedean Property?

Are the computable numbers one example?