My Math Forum Spec(R), dense points

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 April 29th, 2009, 08:49 PM #1 Newbie   Joined: Jan 2009 Posts: 21 Thanks: 0 Spec(R), dense points A point P in a topology for a set $X$ is called dense if P is contained in every non-empty open set of the topology. Alternatively, the closure of $\{P\}$ equals $X$. Find and prove a necessary and sufficient condition for $\text{Spec}(R)$ to have a dense point. The condition should related to the nilradical. How many dense points can $\text{Spec}(R)$ have? I am not seeing how to approach this problem right now. Any helpful hints will be very greatly appreciated. Thank you.

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