Class number

Summary

The class number $h_K$ of a number field $K$ is the order of its ideal class group. It is always finite, and $h_K = 1$ exactly when the ring of integers $\mathcal{O}_K$ is a principal ideal domain, equivalently a unique factorisation domain. Class numbers appear in the class number formula, and the question of which fields have a given class number is the class number problem.