"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": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
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          "source": "w"
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          "kind": "other",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Ring theory",
          "orig": "en:Ring theory",
          "parents": [],
          "source": "w"
        }
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              44,
              56
            ]
          ],
          "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.",
          "type": "example"
        }
      ],
      "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"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with usage examples",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Algebra",
        "en:Ring theory"
      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              44,
              56
            ]
          ],
          "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.",
          "type": "example"
        }
      ],
      "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"
}