This is my attempt.

The basic open set in X = Spec(R), denoted as for , is the collection of prime ideals in X = Spec(R) that do not contain f. For example, if is a unit, then (Similary, is an empty set if f is nilpotent).

Thus, , where V({f}) denotes the variety of {f}.

Any open set in Spec(R) is the union of the above basic open sets. Any open set is a union of an empty set and itself. Since is an empty set if f is a nilpotent, a set of all nilpotent elements, which is a nilradical, is a dense point of Spec(R) (Every prime ideal in Spec(R) contains a nilradical).