"Boolean ring" meaning in English

{
  "etymology_text": "Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.",
  "forms": [
    {
      "form": "Boolean rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Boolean ring (plural Boolean rings)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
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            "Formal sciences",
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            "Fundamental"
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Ring theory",
          "orig": "en:Ring theory",
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            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        }
      ],
      "examples": [
        {
          "text": "From the defining idempotency property of a Boolean ring it is possible to prove that such ring has to have the further properties that each element is its own inverse and that such ring must be commutative."
        }
      ],
      "glosses": [
        "A ring whose multiplicative operation is idempotent."
      ],
      "hypernyms": [
        {
          "word": "linear algebra"
        }
      ],
      "id": "en-Boolean_ring-en-noun-g4-jEF4P",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "multiplicative operation",
          "multiplicative operation"
        ],
        [
          "idempotent",
          "idempotent"
        ]
      ],
      "raw_glosses": [
        "(algebra) A ring whose multiplicative operation is idempotent."
      ],
      "related": [
        {
          "word": "Boolean algebra"
        },
        {
          "word": "ring sum normal form"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Boolean ring",
        "George Boole"
      ]
    }
  ],
  "word": "Boolean ring"
}

{
  "etymology_text": "Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.",
  "forms": [
    {
      "form": "Boolean rings",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Boolean ring (plural Boolean rings)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "linear algebra"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Boolean algebra"
    },
    {
      "word": "ring sum normal form"
    }
  ],
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      "examples": [
        {
          "text": "From the defining idempotency property of a Boolean ring it is possible to prove that such ring has to have the further properties that each element is its own inverse and that such ring must be commutative."
        }
      ],
      "glosses": [
        "A ring whose multiplicative operation is idempotent."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "multiplicative operation",
          "multiplicative operation"
        ],
        [
          "idempotent",
          "idempotent"
        ]
      ],
      "raw_glosses": [
        "(algebra) A ring whose multiplicative operation is idempotent."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Boolean ring",
        "George Boole"
      ]
    }
  ],
  "word": "Boolean ring"
}