"associative algebra" meaning in All languages combined

See associative algebra on Wiktionary

Noun [English]

Forms: associative algebras [plural]
Head templates: {{en-noun}} associative algebra (plural associative algebras)
  1. (algebra) An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative. Wikipedia link: associative algebra Categories (topical): Algebra Synonyms: linear algebra
    Sense id: en-associative_algebra-en-noun-8lZl9k1W Categories (other): English entries with incorrect language header Topics: algebra, mathematics, sciences

Inflected forms

Download JSON data for associative algebra meaning in All languages combined (1.3kB)

{
  "forms": [
    {
      "form": "associative algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "associative algebra (plural associative algebras)",
      "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": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative."
      ],
      "id": "en-associative_algebra-en-noun-8lZl9k1W",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebra over a ring",
          "algebra over a ring"
        ],
        [
          "algebra over a field",
          "algebra over a field"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "product",
          "product"
        ],
        [
          "associative",
          "associative"
        ]
      ],
      "raw_glosses": [
        "(algebra) An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative."
      ],
      "synonyms": [
        {
          "word": "linear algebra"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "associative algebra"
      ]
    }
  ],
  "word": "associative algebra"
}
{
  "forms": [
    {
      "form": "associative algebras",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "associative algebra (plural associative algebras)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "glosses": [
        "An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebra over a ring",
          "algebra over a ring"
        ],
        [
          "algebra over a field",
          "algebra over a field"
        ],
        [
          "bilinear",
          "bilinear"
        ],
        [
          "product",
          "product"
        ],
        [
          "associative",
          "associative"
        ]
      ],
      "raw_glosses": [
        "(algebra) An algebra over a ring (or more narrowly, an algebra over a field) whose bilinear product is associative."
      ],
      "synonyms": [
        {
          "word": "linear algebra"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "associative algebra"
      ]
    }
  ],
  "word": "associative algebra"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-23 from the enwiktionary dump dated 2024-06-20 using wiktextract (1b9bfc5 and 0136956). 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.