Cohen-Macaulay

adjective

Such that its depth is equal to its Krull dimension.

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Meanings

adjectiveCohen-Macaulay (not comparable)
  1. not comparablecommutative algebraSuch that its depth is equal to its Krull dimension.
  2. not comparablecommutative algebraCohen-Macaulay as a module over itself.
  3. not comparablecommutative algebraSuch that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
  4. not comparablecommutative algebraCohen-Macaulay as a module over itself.

Origin

Named for Irvin Cohen and Francis Sowerby Macaulay, who proved unmixedness results for specific classes of rings, which Cohen-Macaulay rings generalize.

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Cite this entry
APA

Cohen-Macaulay. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Cohen-Macaulay

MLA

“Cohen-Macaulay.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Cohen-Macaulay. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Cohen-Macaulay,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Cohen-Macaulay.

Source: Cohen-Macaulay on Wiktionary, CC BY-SA 4.0.