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Primary decomposition

In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by Emanuel Lasker (1905) for…

Measurement, Primary decomposition of an ideal & Overview

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Primary decomposition of an ideal

Commutative ringProper idealZero-divisorQuotientRadical
18 related topics

Overview

MathematicsNoetherian ringPrimary idealsPrime idealsEmanuelLasker
27 related topics

Primary decomposition from associated primes

BourbakiAnnihilatorExact sequenceSupportFinite set
5 related topics

Properties of associated primes

EndomorphismBijectionFinite lengthRing homomorphismFlat
5 related topics

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Overview

Primary decomposition of an ideal

Primary decomposition from associated primes

Properties of associated primes

Non-Noetherian case

Additive theory of ideals

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Primary decomposition

Nodes64
Edges63
Triples81
Avg. degree1.97
Density0.03125
Components1

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Primary decomposition

Top relations

related to References · 57
Primary decomposition → Addison, Algèbre, American Journal, Ann, Atiyah, Bereichen, Berlin, BF01181179, BF01206635, BF01447495, BF01464225Curtis, Bourbaki, Charles, Communications, Commutative, Commutative Algebra, Computer Algebra, David, Die Frage, Emmy
related to Primary decomposition from associated primes · 7
Primary decomposition → Algèbre, Ann, Bourbaki's, By, Equivalently, Let, Nowadays
related to Primary decomposition of an ideal · 6
Primary decomposition → An, Let, Noetherian, R/I, The, Then
related to Non-Noetherian case · 4
Primary decomposition → Let, The, Then, Theorem
related to External links · 3
Primary decomposition → August, Is, MathOverflow
related to Examples · 2
Primary decomposition → All, The
related to Geometric interpretation · 2
Primary decomposition → An, In

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displaystyle primary prime ideal decomposition ideals ring associated set primes theorem mathfrak noetherian minimal rings generated ass every finitely operatorname

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SubjectPredicateObjectConfidenceSrc
Primary decompositionrelated to ExamplesThe0.60section
Primary decompositionrelated to ExamplesAll0.60section
Primary decompositionrelated to External linksIs0.60section
Primary decompositionrelated to External linksMathOverflow0.60section
Primary decompositionrelated to External linksAugust0.60section
Primary decompositionrelated to Geometric interpretationIn0.60section
Primary decompositionrelated to Geometric interpretationAn0.60section
Primary decompositionrelated to Non-Noetherian caseThe0.60section
Primary decompositionrelated to Non-Noetherian caseTheorem0.60section
Primary decompositionrelated to Non-Noetherian caseLet0.60section
Primary decompositionrelated to Non-Noetherian caseThen0.60section
Primary decompositionrelated to Primary decomposition from associated primesNowadays0.60section

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