"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"
        },
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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"
      ],
      "translations": [
        {
          "code": "pl",
          "lang": "Polish",
          "lang_code": "pl",
          "sense": "in a venial manner",
          "tags": [
            "inanimate",
            "masculine"
          ],
          "word": "pierścień Boole'a"
        }
      ],
      "wikipedia": [
        "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": [
    {
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        "English multiword terms",
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        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Polish translations",
        "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": [
        "George Boole"
      ]
    }
  ],
  "translations": [
    {
      "code": "pl",
      "lang": "Polish",
      "lang_code": "pl",
      "sense": "in a venial manner",
      "tags": [
        "inanimate",
        "masculine"
      ],
      "word": "pierścień Boole'a"
    }
  ],
  "word": "Boolean ring"
}