Spectrum of a ring

In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by ${\displaystyle \operatorname {Spec} (R)}$, is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space. A ringed space of this form is called an affine scheme.

For any ideal I of R, define ${\displaystyle V_{I}}$ to be the set of prime ideals containing I. We can put a topology on ${\displaystyle \operatorname {Spec} (R)}$ by defining the collection of closed sets to be

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