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Cohen-Macaulay

Cohen-Macaulay adjective: such that its depth is equal to its Krull dimension.

Adjective

Cohen-Macaulay (not comparable)

  1. (commutative algebra) Such that its depth is equal to its Krull dimension.
  2. (commutative algebra) Cohen-Macaulay as a module over itself.
  3. (commutative algebra) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial.
  4. (commutative algebra) Cohen-Macaulay as a module over itself.

Origin of Cohen-Macaulay

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

Questions about Cohen-Macaulay

What does Cohen-Macaulay mean?
Cohen-Macaulay means such that its depth is equal to its Krull dimension.
What part of speech is Cohen-Macaulay?
Cohen-Macaulay is an adjective.

Words near Cohen-Macaulay in the dictionary

  1. cohemolysin
  2. cohemolysins
  3. cohemolytic
  4. cohen
  5. Cohen syndrome
  6. Cohen-Macaulay
  7. Cohen-Sutherland algorithm
  8. cohencidence
  9. cohencidences
  10. cohencidental
  11. Cohenesque

Source and license

Adapted from Wiktionary: Cohen-Macaulay (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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