prime spectrum of a commutative ring

交换环的素谱空间

Algebra & Algebraic Geometry · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The set of prime ideals of RR with closed sets V(I)={p:I⊆p}V(I)=\{\mathfrak p:I\subseteq\mathfrak p\}.

以素理想为点、以包含指定理想的素理想集合为闭集的拓扑空间。

Example

Spec⁡Z\operatorname{Spec}\mathbb Z contains (0)(0) and each (p)(p).

Usage and distinctions

This is an algebraic prime spectrum, distinct from operator spectra and topological spectra.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. J. S. Milne — A Primer of Commutative Algebra§14 The spectrum of a ring, Definition before Proposition 14.1 and paragraph after its proof defining the Zariski topology, printed p.63 / PDF p.63 · Checked 2026-10-15

Translation sources

  1. 许金兴 — 交换代数讲义（作者讲义，USTC 评课社区托管）§1.2 素谱空间, Definition 1.2.1 · Checked 2026-10-14
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