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**pascal4542** A point P in a topology for a set $\displaystyle X$ is called dense if P is contained in every non-empty open set of the topology. Alternatively, the closure of $\displaystyle \{P\}$ equals $\displaystyle X$.

Find and prove a necessary and sufficient condition for $\displaystyle \text{Spec}(R)$ to have a dense point. The condition should related to the nilradical. How many dense points can $\displaystyle \text{Spec}(R)$ have?

I am not seeing how to approach this problem right now. Any helpful hints will be very greatly appreciated. Thank you.