Artin-Schreier Extensions
We are interested in a special category of field extensions. Let $K$ be a field of characteristic $p \ne 0$, we want to know the structure of an extension of $K$ of degree $p$. It turns out that there lies the an Artin-Schreier polynomial of the form $X^p-X-\alpha$.
Artin-Schreier Extensions
Equivalent Conditions of Regular Local Rings of Dimension 1
In this post we collect and prove (as detailed as possible) the equivalent conditions of being a Regular local ring of dimension 1.
Equivalent Conditions of Regular Local Rings of Dimension 1