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Krull dimension

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of…

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Krull dimension

Nodes77
Edges76
Triples40
Avg. degree1.97
Density0.025974
Components1

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Krull dimension

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related to Examples · 18
Krull dimension → An, Artinian, Cohen, Dedekind, For, Given, If, In, Krull, Let, Macaulay, More, Neumann, Noether, Noetherian, The, The Krull, Then
related to Explanation · 7
Krull dimension → Given, In, Krull, That, The, The Krull, We
related to Schemes · 6
Krull dimension → Galois, It, Krull, Spec, This, Zariski
related to Of a module · 5
Krull dimension → Ann, End, If, Krull, That
related to For non-commutative rings · 4
Krull dimension → For, Noetherian, The, The Krull

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dimension ring krull noetherian ideal prime displaystyle ideals rings field height commutative algebra chains supremum isbn mathfrak zero lengths algebraic

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SubjectPredicateObjectConfidenceSrc
Krull dimensionrelated to ExamplesThe0.60section
Krull dimensionrelated to ExamplesIn0.60section
Krull dimensionrelated to ExamplesNoetherian0.60section
Krull dimensionrelated to ExamplesIf0.60section
Krull dimensionrelated to ExamplesFor0.60section
Krull dimensionrelated to ExamplesGiven0.60section
Krull dimensionrelated to ExamplesMore0.60section
Krull dimensionrelated to ExamplesAn0.60section
Krull dimensionrelated to ExamplesKrull0.60section
Krull dimensionrelated to ExamplesDedekind0.60section
Krull dimensionrelated to ExamplesThe Krull0.60section
Krull dimensionrelated to ExamplesArtinian0.60section

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