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Spectrum of a ring

In mathematics, and more specifically in commutative algebra and algebraic geometry, the prime spectrum (or simply the spectrum) of a commutative ring R {\displaystyle R} is the set of all prime ideals of R , {\displaystyle R,} equipped with a topology called the Zariski topology. The spectrum of a commutative ring is naturally endowed with a sheaf of…

History, Historical motivation & Affine schemes

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Overview

Historical motivation

Zariski topology

Affine schemes

Motivation from algebraic geometry

Examples

Non-affine examples

Non-Zariski topologies on a prime spectrum

Global or relative Spec

Representation theory perspective

Functional analysis perspective

Similar concepts

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Map overview Semantic statistics

Spectrum of a ring

Nodes136
Edges135
Triples13
Avg. degree1.99
Density0.014706
Components1

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Spectrum of a ring

Top relations

related to Representation theory perspective · 7
Spectrum of a ring → As, From, R-module, R/I, Recall, The, Then
related to Historical motivation · 6
Spectrum of a ring → Alexander Grothendieck, It, One, The, This, Zariski

Important terminology Word statistics

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Important terminology

displaystyle ring spec operatorname affine ideals spectrum mathcal prime space set mathbb open scheme algebraic sheaf schemes sets ideal closed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Spectrum of a ringrelated to Historical motivationThe0.60section
Spectrum of a ringrelated to Historical motivationAlexander Grothendieck0.60section
Spectrum of a ringrelated to Historical motivationIt0.60section
Spectrum of a ringrelated to Historical motivationOne0.60section
Spectrum of a ringrelated to Historical motivationZariski0.60section
Spectrum of a ringrelated to Historical motivationThis0.60section
Spectrum of a ringrelated to Representation theory perspectiveFrom0.60section
Spectrum of a ringrelated to Representation theory perspectiveR/I0.60section
Spectrum of a ringrelated to Representation theory perspectiveRecall0.60section
Spectrum of a ringrelated to Representation theory perspectiveThe0.60section
Spectrum of a ringrelated to Representation theory perspectiveAs0.60section
Spectrum of a ringrelated to Representation theory perspectiveThen0.60section

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    Min side: 3
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