Example of a Dedekind domain that has only finitely many prime ideals, and is not a field?
Any help would be greatly appreciated!
Example of a Dedekind domain that has only finitely many prime ideals, and is not a field?
Any help would be greatly appreciated!
Very simply, $\mathbb Z_{(2)} = $ ring of all rationals with odd denominator, or any DVR (local PID not a field)
Recall that Dedekind domains may be thought of as globalizations of DVRs since for local domains we have Dedekind $\iff$ PID $\iff$ DVR