Definition:Prime Ideal of Number Field
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Definition
Let $K$ be a number field.
Let $\OO_K$ be its ring of integers.
Let $\mathfrak p \subseteq \OO_K$ be an ideal.
Then $\mathfrak p$ is a prime ideal if and only if it is not the unit ideal $\ideal 1$ and $\mathfrak p$ has no divisors other than $\mathfrak p$ and $\ideal 1$.
Also see
Generalizations
Sources
- 1981: Erich Hecke: Lectures on the Theory of Algebraic Numbers: $\S24$: Definition and Basic Properties of Ideals