{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:b1e9ae23-1814-48c8-8a33-0b0337c674d8",
  "labels": {
    "zh-CN": "交换环（Szekeres约定）",
    "en": "commutative ring"
  },
  "alternative_labels": [
    {
      "lang": "en",
      "value": "ring"
    },
    {
      "lang": "zh-CN",
      "value": "环"
    }
  ],
  "scope_note": "§3.1 explicitly assumes (R6) ab=ba; identity is not required.",
  "identity_status": "active",
  "identity_revision": "4da970a6bcdc4f521ad903d141c968461db33821f03a3fea39ef05c8b5e99fa2",
  "occurrences": [
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      "concept_id": "urn:uuid:b1e9ae23-1814-48c8-8a33-0b0337c674d8",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-03/01-rings-and-fields",
      "anchor": "concept-3-ring",
      "chapter": "3",
      "section": "3.1",
      "offset": 331,
      "range": [
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        4337
      ],
      "source_revision": "e45fecab51d11049987b1cd993cbcceb38e261c7f113a34cebc31a82bb2c8227",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "环(ring)",
      "context": {
        "range": [
          4123,
          4468
        ],
        "quote": "一个 <u id=\"concept-3-ring\" class=\"concept-term\" data-concept-identity=\"urn:uuid:b1e9ae23-1814-48c8-8a33-0b0337c674d8\" data-concept-route=\"/concept-identities#concept-b1e9ae23-1814-48c8-8a33-0b0337c674d8\">环(ring)</u> $R$ 是一个集合，带有两种复合运算，分别称为加法和乘法，记作 $a + b$ 和 $a b$。要求 $R$ 关于 $+$ 构成阿贝尔群，其恒等元为 $0$，逆元记作 $-a$。关于乘法，$R$ 应为交换半群，因而恒等元和逆元未必存在。具体而言，环的要求如下：",
        "quote_sha256": "c5d9f721b2809a73283a85f68a8dc6c384e108cf5e496926aac62bfe7f9b06a7",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-03/01-rings-and-fields",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-28b2b6679eac4181e54894d1"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-03/01-rings-and-fields",
      "lang": "zh-CN",
      "section": "3.1",
      "signal": "term-mark",
      "label": "环",
      "english": "ring",
      "offset": 331
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-28b2b6679eac4181e54894d1"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "0a0d7a6ba242dbf4b15c8ef55bb69c2b25abca25602a79c1b54f07a4638752a6",
  "optional_enrichments": []
}