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Exponents of Prime Ideals in Number Fields

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 […]