All Questions

Let $K=\mathbb Q(\theta)$ be a number field with integral primitive element $\theta$, and let $f(x)$ be the minimal polynomial of $\theta$. Let $p$ be a rational prime. It's well known that if $p$ ...

Given a number field $K$, I would like to compute (in Sage) generators for the group of totally positive units of $K$. Update: I've tried some code (details below), which I've received some help on in ...

Let $k$ be a given number field. What is the importance and applications of knowing that the Iwasawa module $X_\infty$ of $k$ is an elementary $\Lambda$-module?

Let $K$ be the Number field and $L$ be finite extension where $\mathfrak{p}$ prime of K is unramified. Are there any conditions on $\mathfrak{p}$ so that I can say $\mathfrak{p}$ splits completely in ...