"Cohen-Macaulay" meaning in All languages combined

See Cohen-Macaulay on Wiktionary

Adjective [English]

Etymology: Named for Irvin Cohen and Francis Sowerby Macaulay, who proved unmixedness results for specific classes of rings, which Cohen-Macaulay rings generalize. Head templates: {{en-adj|-}} Cohen-Macaulay (not comparable)
  1. (commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension. Tags: not-comparable Categories (topical): Algebra
    Sense id: en-Cohen-Macaulay-en-adj-en:module Disambiguation of Algebra: 28 21 30 21 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 34 13 39 13 Disambiguation of Pages with 1 entry: 33 15 36 15 Disambiguation of Pages with entries: 32 15 38 15
  2. (commutative algebra, of a noetherian local ring) Cohen-Macaulay as a module over itself. Tags: not-comparable Categories (topical): Algebra
    Sense id: en-Cohen-Macaulay-en-adj-sV0Mz~Gk Disambiguation of Algebra: 28 21 30 21 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 34 13 39 13 Disambiguation of Pages with 1 entry: 33 15 36 15 Disambiguation of Pages with entries: 32 15 38 15
  3. (commutative algebra, of a module M over a noetherian ring) Such that all localizations of M at maximal ideals contained in the support of M are either Cohen-Macaulay or trivial. Tags: not-comparable Categories (topical): Algebra
    Sense id: en-Cohen-Macaulay-en-adj-en:module2 Disambiguation of Algebra: 28 21 30 21 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 34 13 39 13 Disambiguation of Pages with 1 entry: 33 15 36 15 Disambiguation of Pages with entries: 32 15 38 15
  4. (commutative algebra, of a noetherian ring) Cohen-Macaulay as a module over itself. Tags: not-comparable Categories (topical): Algebra
    Sense id: en-Cohen-Macaulay-en-adj-sV0Mz~Gk1 Disambiguation of Algebra: 28 21 30 21 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 34 13 39 13 Disambiguation of Pages with 1 entry: 33 15 36 15 Disambiguation of Pages with entries: 32 15 38 15

Alternative forms

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  "etymology_text": "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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        "Such that its depth is equal to its Krull dimension."
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          "Krull dimension",
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      "raw_glosses": [
        "(commutative algebra, of a finite module over a noetherian local ring) Such that its depth is equal to its Krull dimension."
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      "raw_tags": [
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      "raw_tags": [
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      "tags": [
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}
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}

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