principal ideal in English

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{
  "forms": [
    {
      "form": "principal ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "principal ideal (plural principal ideals)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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            "Entry maintenance"
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          "source": "w"
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
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            "Formal sciences",
            "Sciences",
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            "Fundamental"
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          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "left principal ideal"
        },
        {
          "word": "principal fractional ideal"
        },
        {
          "word": "principal ideal domain"
        },
        {
          "word": "right principal ideal"
        }
      ],
      "glosses": [
        "An ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a."
      ],
      "id": "en-principal_ideal-en-noun-u2iAcL3G",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ideal",
          "ideal"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "semigroup",
          "semigroup"
        ],
        [
          "lattice",
          "lattice"
        ],
        [
          "generated",
          "generated"
        ]
      ],
      "raw_glosses": [
        "(algebra) An ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a."
      ],
      "synonyms": [
        {
          "sense": "smallest ideal that contains a given element",
          "word": "two-sided principal ideal"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "principal ideal"
      ]
    }
  ],
  "word": "principal ideal"
}

[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
  "derived": [
    {
      "word": "left principal ideal"
    },
    {
      "word": "principal fractional ideal"
    },
    {
      "word": "principal ideal domain"
    },
    {
      "word": "right principal ideal"
    }
  ],
  "forms": [
    {
      "form": "principal ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "principal ideal (plural principal ideals)",
      "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 ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ideal",
          "ideal"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "semigroup",
          "semigroup"
        ],
        [
          "lattice",
          "lattice"
        ],
        [
          "generated",
          "generated"
        ]
      ],
      "raw_glosses": [
        "(algebra) An ideal I in an algebraic object R (which could be a ring, algebra, semigroup or lattice) that is generated by a given single element a ∈ R; the smallest ideal that contains a."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "principal ideal"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "smallest ideal that contains a given element",
      "word": "two-sided principal ideal"
    }
  ],
  "word": "principal ideal"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c and c9440ce). 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.

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"principal ideal" meaning in English

Noun

Inflected forms