"multiplicative subset" meaning in English

{
  "forms": [
    {
      "form": "multiplicative subsets",
      "tags": [
        "plural"
      ]
    }
  ],
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      "expansion": "multiplicative subset (plural multiplicative subsets)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "text": "If P is a proper prime ideal of a ring and M is the set complement, w.r.t. the ring, of P, then M is a multiplicative subset.",
          "type": "example"
        }
      ],
      "glosses": [
        "A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation."
      ],
      "id": "en-multiplicative_subset-en-noun-AqnT9M2i",
      "links": [
        [
          "ring",
          "ring"
        ],
        [
          "unity",
          "unity"
        ]
      ],
      "qualifier": "commutative algebra",
      "raw_glosses": [
        "(commutative algebra) A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation."
      ],
      "wikipedia": [
        "multiplicatively closed set"
      ]
    }
  ],
  "word": "multiplicative subset"
}

{
  "forms": [
    {
      "form": "multiplicative subsets",
      "tags": [
        "plural"
      ]
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  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "text": "If P is a proper prime ideal of a ring and M is the set complement, w.r.t. the ring, of P, then M is a multiplicative subset.",
          "type": "example"
        }
      ],
      "glosses": [
        "A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation."
      ],
      "links": [
        [
          "ring",
          "ring"
        ],
        [
          "unity",
          "unity"
        ]
      ],
      "qualifier": "commutative algebra",
      "raw_glosses": [
        "(commutative algebra) A subset of a ring which contains the ring’s unity and which is multiplicatively closed, i.e., it is closed with respect to the ring’s multiplicative operation."
      ],
      "wikipedia": [
        "multiplicatively closed set"
      ]
    }
  ],
  "word": "multiplicative subset"
}