Definition 10.17.1. Let R be a ring.
The spectrum of R is the set of prime ideals of R. It is usually denoted \mathop{\mathrm{Spec}}(R).
Given a subset T \subset R we let V(T) \subset \mathop{\mathrm{Spec}}(R) be the set of primes containing T, i.e., V(T) = \{ \mathfrak p \in \mathop{\mathrm{Spec}}(R) \mid \forall f\in T, f\in \mathfrak p\} .
Given an element f \in R we let D(f) \subset \mathop{\mathrm{Spec}}(R) be the set of primes not containing f.
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