I have a question about “factoring out” common prime ideal factors in a number field. Let $K$ be a number field with ring of integers $\mathcal{O}_K$. Let $\mathfrak{p}$ be a prime ideal of $\mathcal{O}_K$. Now let $k \in K$. I know I can write $k = a/b$ for $a,b \in \mathcal{O}_K$. Now consider the fractional […]

Categories

## Exponents of Prime Ideals in Number Fields

- Post author By Q+A Expert
- Post date March 26, 2020
- No Comments on Exponents of Prime Ideals in Number Fields

- Tags are we able to "factor out" common factors in their prime decomposition?, b \in \mathcal{O}_K$. Now consider the fractional ideal $k\mathcal{O}_K$. Let $v_\mathfrak{p}(x)$ be the exponent that $\mathfrak{p}$ appears, b$ in such a way so that $v_\mathfrak{p}(b) = 0$. So in a way, I have a question about "factoring out" common prime ideal factors in a number field. Let $K$ be a number field with ring of integers $\math, is it always possible to choose $a