"proregular" meaning in All languages combined

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pro",
        "3": "regular"
      },
      "expansion": "pro- + regular",
      "name": "prefix"
    }
  ],
  "etymology_text": "pro- + regular",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "proregular (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms prefixed with pro-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2016, Liran Shaul, “Adic reduction to the diagonal and a relation between cofiniteness and derived completion”, in arXiv",
          "text": "Then adic reduction to the diagonal holds: A#x5C;otimes#x7B;L#x7D;#x5F;#x7B;A#x5C;hat#x7B;#x5C;otimes#x7D;#x7B;L#x7D;#x5F;#x7B;K#x7D;A#x7D;(M#x5C;hat#x7B;#x5C;otimes#x7D;#x7B;L#x7D;#x5F;#x7B;K#x7D;N)#x5C;congM#x5C;otimes#x7B;L#x7D;#x5F;AN. (2) Let A be a commutative ring, let a#x5C;subseteqA be a weakly proregular ideal, let M be an A-module, and assume that the a-adic completion of A is noetherian (if A is noetherian, all these conditions are always satisfied).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)"
      ],
      "id": "en-proregular-en-adj-2uH-P0N~",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "module",
          "module"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "proregular"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pro",
        "3": "regular"
      },
      "expansion": "pro- + regular",
      "name": "prefix"
    }
  ],
  "etymology_text": "pro- + regular",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "proregular (not comparable)",
      "name": "en-adj"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "adj",
  "senses": [
    {
      "categories": [
        "English adjectives",
        "English entries with incorrect language header",
        "English lemmas",
        "English terms prefixed with pro-",
        "English terms with quotations",
        "English uncomparable adjectives",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2016, Liran Shaul, “Adic reduction to the diagonal and a relation between cofiniteness and derived completion”, in arXiv",
          "text": "Then adic reduction to the diagonal holds: A#x5C;otimes#x7B;L#x7D;#x5F;#x7B;A#x5C;hat#x7B;#x5C;otimes#x7D;#x7B;L#x7D;#x5F;#x7B;K#x7D;A#x7D;(M#x5C;hat#x7B;#x5C;otimes#x7D;#x7B;L#x7D;#x5F;#x7B;K#x7D;N)#x5C;congM#x5C;otimes#x7B;L#x7D;#x5F;AN. (2) Let A be a commutative ring, let a#x5C;subseteqA be a weakly proregular ideal, let M be an A-module, and assume that the a-adic completion of A is noetherian (if A is noetherian, all these conditions are always satisfied).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "module",
          "module"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)"
      ],
      "tags": [
        "not-comparable"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "proregular"
}

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  "msg": "gloss may contain unhandled list items: Having the property that the inverse systems of the Koszul cohomology modules satisfy the Inverse limit#Mittag-Leffler condition.)",
  "path": [
    "proregular"
  ],
  "section": "English",
  "subsection": "adjective",
  "title": "proregular",
  "trace": ""
}