Let A be a ring where every prime ideal is maximal. Show that any localization of A/N, where N is a nilradical,with respect to a maximal ideal m is 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 that A/N has also the property that every prime ideal is maximal? because that will solve the problem.