On the distribution of prime ideals within the ideal class group

Robert Gimer, William Heinzer, and William W. Smith

For a countably generated group $K$ and a function $\Delta$ on $K$ taking values that are either nonnegative integers or $\infty$, we determine in Theorem 8 equivalent conditions for there to exist a Dedekind domain $D$ with class group $K$ such that, for each $k$ in $K$, exactly $\Delta(k)$ maximal ideals of $D$ belong to $k$.