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Complete intersection ring

In commutative algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections. Informally, they can be thought of roughly as the local rings that can be defined using the "minimum possible" number of relations.

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Overview

Definition

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Map overview Semantic statistics

Complete intersection ring

Nodes19
Edges18
Triples20
Avg. degree1.89
Density0.105263
Components1

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Complete intersection ring

Top relations

related to Definition · 9
Complete intersection ring → Define, For, H1, If, Koszul, Noetherian, Taking, The, There
related to Counterexample · 7
Complete intersection ring → As, Complete, For, Gorenstein, It, Poincaré, R/I
is a · 2
Complete intersection ring → commutative ring similar to the coordinate rings of varieties that are complete intersections, Noetherian local ring whose completion is the quotient of a regular local ring by an ideal generated by a regular sequence
related to Not a complete intersection · 1
Complete intersection ring → An
related to Regular local rings · 1
Complete intersection ring → Regular

Important terminology Word statistics

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Important terminology

local ring complete rings intersection regular noetherian dimension displaystyle ideal definition embedding maximal called algebra completion quotients m2 first deviation

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Complete intersection ringis acommutative ring similar to the coordinate rings of varieties that are complete intersections0.90text
Complete intersection ringis aNoetherian local ring whose completion is the quotient of a regular local ring by an ideal generated by a regular sequence0.90text
Complete intersection ringrelated to CounterexampleComplete0.60section
Complete intersection ringrelated to CounterexampleGorenstein0.60section
Complete intersection ringrelated to CounterexampleR/I0.60section
Complete intersection ringrelated to CounterexampleAs0.60section
Complete intersection ringrelated to CounterexamplePoincaré0.60section
Complete intersection ringrelated to CounterexampleIt0.60section
Complete intersection ringrelated to CounterexampleFor0.60section
Complete intersection ringrelated to DefinitionNoetherian0.60section
Complete intersection ringrelated to DefinitionTaking0.60section
Complete intersection ringrelated to DefinitionFor0.60section

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    Min side: 3
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