{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0K26YKNBSA"
    },
    {
      "field": "uses",
      "target": "6D8RK0Q6QM"
    },
    {
      "field": "uses",
      "target": "7Q6KK8WJ02"
    },
    {
      "field": "uses",
      "target": "8MGH8PGJWR"
    },
    {
      "field": "uses",
      "target": "8NMGMXNF02"
    },
    {
      "field": "uses",
      "target": "AG4FF4DNYQ"
    },
    {
      "field": "uses",
      "target": "BGXEC1SVQV"
    },
    {
      "field": "uses",
      "target": "DSF8C6QPAG"
    },
    {
      "field": "uses",
      "target": "E1NE8V7EX8"
    },
    {
      "field": "uses",
      "target": "E9QNNPQD2P"
    },
    {
      "field": "uses",
      "target": "VK52XRHBXE"
    },
    {
      "field": "uses",
      "target": "Y1P96JQN34"
    },
    {
      "field": "about",
      "target": "S37DQGW3TZ"
    }
  ],
  "body": "\n## Summary\n\nA zero divisor of a ring is an element that gives zero when you multiply it by some nonzero element.\nThe [[definition of a zero divisor|0K26YKNBSA]] gives the precise condition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "A7EKMZA5XT"
    ],
    "kind": "concept",
    "msc": [
      "16U99"
    ],
    "name": "Zero divisor",
    "same_as": {
      "wikidata": "Q828111",
      "wikipedia": "Zero divisor"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Zero_divisor"
      }
    ],
    "tag": "0NNRDW10RZ"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0NNRDW10RZ/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/0NNRDW10RZ.md",
  "msc": [
    "16U99"
  ],
  "name": "Zero divisor",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0NN/0NNRDW10RZ.md",
  "status": null,
  "tag": "0NNRDW10RZ",
  "uri": "m2://0NNRDW10RZ",
  "url": "https://tamnd.github.io/math2/wiki/zero-divisor/",
  "writing": {
    "tag": "0NNRDW10RZ",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}