"two-sided ideal" meaning in All languages combined

{
  "forms": [
    {
      "form": "two-sided ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "two-sided ideal (plural two-sided 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"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis."
      ],
      "hypernyms": [
        {
          "word": "left ideal"
        },
        {
          "word": "right ideal"
        },
        {
          "word": "subring"
        }
      ],
      "id": "en-two-sided_ideal-en-noun-2CzSOCEu",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subring",
          "subring"
        ],
        [
          "left ideal",
          "left ideal"
        ],
        [
          "right ideal",
          "right ideal"
        ],
        [
          "ideal",
          "ideal"
        ]
      ],
      "raw_glosses": [
        "(algebra) A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis."
      ],
      "synonyms": [
        {
          "word": "ideal"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "two-sided ideal"
}

{
  "forms": [
    {
      "form": "two-sided ideals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "two-sided ideal (plural two-sided ideals)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "left ideal"
    },
    {
      "word": "right ideal"
    },
    {
      "word": "subring"
    }
  ],
  "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": [
        "A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subring",
          "subring"
        ],
        [
          "left ideal",
          "left ideal"
        ],
        [
          "right ideal",
          "right ideal"
        ],
        [
          "ideal",
          "ideal"
        ]
      ],
      "raw_glosses": [
        "(algebra) A subring which is both a left ideal and a right ideal. Commonly referred to simply as an ideal, but referred to as two-sided ideal for emphasis."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "ideal"
    }
  ],
  "word": "two-sided ideal"
}