LetAbe a ring where every prime ideal is maximal. Show that any localization ofA/N, whereNis a nilradical,with respect to a maximal idealmis a field.

Now, it is clear that the above localization will be a reduced ring (since A/N is reduced and localization and operation of taking nilradical commute).

...not sure how to proceed now....can we show somehow thatA/Nhas also the property that every prime ideal is maximal? because that will solve the problem.