The spectrum of a ring is the set of proper prime ideals,
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The classical example is the spectrum of polynomial rings. For instance,
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and
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The points are, in classical algebraic geometry, algebraic varieties. Note that are maximal ideals, hence also prime.
The spectrum of a ring has a topology called the Zariski topology. The closed sets are of the form
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For example,
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Every prime ideal is closed except for , whose closure is .