Blog

2025

Automorphisms of Fields

7 minute read

Published:

We describe some rigidity (or lack thereof) results for field automorphisms. This is based on another problem from my girlfriend’s algebra exam.

Tychonoff’s Theorem via Filters

8 minute read

Published:

To give myself some practice with filters, we describe the proof of Tychonoff’s theorem via filters.

Nets

4 minute read

Published:

For my own personal use, we review the basic theory of nets.

Hilbert’s Nullstellensatz

7 minute read

Published:

We record a proof of the bijection of algebraic sets and radical ideals, using Hilbert’s Nullstellensatz.

The Sign of the Linear Action

8 minute read

Published:

We compute the sign of \(\operatorname{GL}_n(\mathbb F_q)\) acting on \(\mathbb F_q^{\oplus n}\).

Groups With No Automorphisms

2 minute read

Published:

We classify the groups with trivial automorphism groups. This was a pretty tricky problem on my girlfriend’s algebra qualifying exam the other day!