# Tagged Questions

**4**

votes

**4**answers

703 views

### What are the lengths that can be constructed with straightedge but without compass?

Most field theory textbooks will describe the field of constructible numbers, i.e. complex numbers corresponding to points in the Euclidean plane that can be constructed via straightedge and compass. ...

**3**

votes

**1**answer

564 views

### Can the algebraic closure of a complete field be complete and of infinite degree?

Yes, this is yet another "foundational" question in valuation theory.
Here's the background: it is a well known classical fact that the dimension (in the purely algebraic sense) of a real Banach ...

**11**

votes

**2**answers

487 views

### Algebraicity of the completion of a field? Finiteness?

At the end of my 8410 class today (see http://www.math.uga.edu/~pete/MATH8410.html if you care), one of my students asked me the following very interesting question:
Let $(K,|\ |)$ be a normed field, ...

**13**

votes

**2**answers

597 views

### What is the prime spectrum of a Cauchy series ring?

Let $k$ be a field, and let $| \ |$ be a norm on $k$. The norm induces a metric. To construct the completion $\hat{k}$ as a normed field, the standard recipe is to take the quotient of the ring ...