"Auslander-Reiten theory" meaning in All languages combined

See Auslander-Reiten theory on Wiktionary

Noun [English]

Etymology: Introduced by Maurice Auslander and Idun Reiten (1975). Head templates: {{en-noun|-}} Auslander-Reiten theory (uncountable)
  1. (algebra) The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers. Tags: uncountable Categories (topical): Algebra
    Sense id: en-Auslander-Reiten_theory-en-noun-iIFKxUye Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: algebra, mathematics, sciences
{
  "etymology_text": "Introduced by Maurice Auslander and Idun Reiten (1975).",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "Auslander-Reiten theory (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers."
      ],
      "id": "en-Auslander-Reiten_theory-en-noun-iIFKxUye",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "representation theory",
          "representation theory"
        ],
        [
          "Artinian",
          "Artinian"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "technique",
          "technique"
        ],
        [
          "Auslander-Reiten sequence",
          "Auslander-Reiten sequence"
        ],
        [
          "almost split sequence",
          "almost split sequence"
        ],
        [
          "Auslander-Reiten quiver",
          "Auslander-Reiten quiver"
        ]
      ],
      "raw_glosses": [
        "(algebra) The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Auslander-Reiten theory"
}
{
  "etymology_text": "Introduced by Maurice Auslander and Idun Reiten (1975).",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "Auslander-Reiten theory (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Algebra"
      ],
      "glosses": [
        "The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "representation theory",
          "representation theory"
        ],
        [
          "Artinian",
          "Artinian"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "technique",
          "technique"
        ],
        [
          "Auslander-Reiten sequence",
          "Auslander-Reiten sequence"
        ],
        [
          "almost split sequence",
          "almost split sequence"
        ],
        [
          "Auslander-Reiten quiver",
          "Auslander-Reiten quiver"
        ]
      ],
      "raw_glosses": [
        "(algebra) The study of the representation theory of Artinian rings using techniques such as Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Auslander-Reiten theory"
}

Download raw JSONL data for Auslander-Reiten theory meaning in All languages combined (1.3kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.