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In abstract algebra and algebraic geometry, the spectrum of a commutative ring ''R'', denoted by 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. ==Zariski topology== For any ideal ''I'' of ''R'', define to be the set of prime ideals containing ''I''. We can put a topology on Spec(''R'') by defining the collection of closed sets to be : This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For ''f''∈''R'', define ''D''''f'' to be the set of prime ideals of ''R'' not containing ''f''. Then each ''D''''f'' is an open subset of Spec(''R''), and is a basis for the Zariski topology. Spec(''R'') is a compact space, but almost never Hausdorff: in fact, the maximal ideals in ''R'' are precisely the closed points in this topology. However, Spec(''R'') is always a Kolmogorov space. It is also a spectral space. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「spectrum of a ring」の詳細全文を読む スポンサード リンク
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