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I have a small problem on the number of generators of ideal and class number.

Let $F$ be a number field with class number $h_F$. If $h_F=1$ then every ideal of $F$ is princile ideal.
Assume $h_F>1$. Can we say that the number of generators of ideals of $F$ is at most $h_F$? If it is true, where can I find a proof?

Thanks!

Qinghua Pi
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1 Answers1

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Actually, it turns out that the number of generators of ideas of $F$ is at most $2$! Rings of integers in number fields are "Dedekind domains", and Dedekind domains have this property. Knowing the words "Dedekind domain" should allow you to search for all kinds of relevant information; this math.stackexchange question is relevant, for example.

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Greg Martin
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