Krull dimension

noun

The supremum of the lengths of all chains of prime ideals.

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Meanings

nounKrull dimension (uncountable)
  1. uncountablecommutative algebraThe supremum of the lengths of all chains of prime ideals.

Origin

Named for Wolfgang Krull, for his work on the height of finitely generated ideals of noetherian rings. The term dimension is from the correspondence between the geometric dimension of an affine variety and the Krull dimension of its coordinate ring.

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Cite this entry
APA

Krull dimension. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Krull%20dimension

MLA

“Krull dimension.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Krull%20dimension. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Krull dimension,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Krull%20dimension.

Source: Krull dimension on Wiktionary, CC BY-SA 4.0.