"left ideal" meaning in English

{
  "forms": [
    {
      "form": "left ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "left ideal (plural left ideals)",
      "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"
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          "source": "w"
        },
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          "source": "w"
        },
        {
          "kind": "other",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "coordinate_terms": [
        {
          "word": "right ideal"
        }
      ],
      "examples": [
        {
          "text": "If I is a left ideal of R then rI⊆I for any r isin R."
        }
      ],
      "glosses": [
        "A subset of a ring which is closed under left-multiplication by any element of the ring."
      ],
      "hyponyms": [
        {
          "word": "two-sided ideal"
        }
      ],
      "id": "en-left_ideal-en-noun-Ru-76cX-",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "closed",
          "closed"
        ],
        [
          "multiplication",
          "multiplication"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebra) A subset of a ring which is closed under left-multiplication by any element of the ring."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "left ideal"
}

{
  "coordinate_terms": [
    {
      "word": "right ideal"
    }
  ],
  "forms": [
    {
      "form": "left ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "left ideal (plural left ideals)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "two-sided ideal"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
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        "English nouns",
        "Pages with 1 entry",
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        "en:Algebra"
      ],
      "examples": [
        {
          "text": "If I is a left ideal of R then rI⊆I for any r isin R."
        }
      ],
      "glosses": [
        "A subset of a ring which is closed under left-multiplication by any element of the ring."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subset",
          "subset"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "closed",
          "closed"
        ],
        [
          "multiplication",
          "multiplication"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebra) A subset of a ring which is closed under left-multiplication by any element of the ring."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "left ideal"
}