{
"schema_version": 1,
"kind": "ConceptView",
"producer": "concept-view-1",
"concept_id": "urn:uuid:fc4d4ed6-1e21-45ac-81f8-30621814489a",
"labels": {
"zh-CN": "有限生成阿贝尔群",
"en": "finitely generated Abelian group"
},
"alternative_labels": [
{
"lang": "en",
"value": "finitely generated"
}
],
"scope_note": "原书3.1.2中由有限多个元素整系数生成的阿贝尔群；与自由阿贝尔群及其结构定理不同。管理员核对的原书定义/陈述；不声明首次出现，不把Theorem环境伪作Definition编号。",
"identity_status": "active",
"identity_revision": "5426bafd4c81b6fad25c122c7a9377c5b86b620399fb80c52f52dc63be04f125",
"occurrences": [
{
"concept_id": "urn:uuid:fc4d4ed6-1e21-45ac-81f8-30621814489a",
"book_id": "nakahara-geometry-topology-physics",
"edition_id": "second-edition-local",
"lang": "zh-CN",
"route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/01-section-3-1",
"anchor": "bound-first-679c7c1d12787a3042264340",
"chapter": "3",
"section": "3.1",
"offset": 1142,
"range": [
15177,
15651
],
"source_revision": "8c227052a7dbfe622e71625cd78cab83dfb97f5703f66636a4ca4fc6fc24676b",
"source_category": "machine_draft",
"review_status": "unreviewed",
"role": "first-mention",
"role_basis": {
"kind": "explicit-source-uuid-marker",
"source_bound_role": "first-mention",
"first_mention": true,
"source_node": "a-5807fd273f1bd596a5049548",
"source_sidecar": {
"path": "library/books/nakahara-geometry-topology-physics/second-edition-local/provenance/chapter-03/concept-annotations.json",
"sha256": "6cea3dacb311fa37962312627466368359a7e6a27a452b3c1e498fb373af3a2a",
"page": "3.1",
"annotation_count": 31,
"policy": "explicit-source-bound-UUIDs; no string-based identity allocation",
"rendered_annotation_count": 20,
"plain_mention_count": 11,
"display_policy": "clickable-only"
}
},
"label": "有限生成阿贝尔群",
"context": {
"range": [
14159,
17746
],
"quote": null,
"quote_sha256": "f4e47dc267d2e547cc4ddb84cc95b05c3caf324448938c70328ff310b162cf9f",
"environment": null,
"excerpt_omitted": true
},
"parallel_readings": [
{
"route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/01-section-3-1",
"lang": "en",
"source_category": "machine_draft",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-8d1b6bead38429222a6d2976"
},
{
"concept_id": "urn:uuid:fc4d4ed6-1e21-45ac-81f8-30621814489a",
"book_id": "nakahara-geometry-topology-physics",
"edition_id": "second-edition-local",
"lang": "zh-CN",
"route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/03-section-3-3",
"anchor": "bound-mention-fe0fb08fcff4bd0db9418e50",
"chapter": "3",
"section": "3.3",
"offset": 5799,
"range": [
36342,
36981
],
"source_revision": "8017bf8af64322ac183f2df92052a1b4911ac0a6339fd2a7b7c394e79cf835d4",
"source_category": "machine_draft",
"review_status": "unreviewed",
"role": "discussion",
"role_basis": {
"kind": "explicit-source-uuid-marker",
"source_bound_role": "discussion",
"first_mention": false,
"source_node": "a-27724e61bb9a37f92b8e264c",
"source_sidecar": {
"path": "library/books/nakahara-geometry-topology-physics/second-edition-local/provenance/chapter-03/concept-annotations.json",
"sha256": "6cea3dacb311fa37962312627466368359a7e6a27a452b3c1e498fb373af3a2a",
"page": "3.3",
"annotation_count": 83,
"policy": "explicit-source-bound-UUIDs; no string-based identity allocation",
"rendered_annotation_count": 45,
"plain_mention_count": 38,
"display_policy": "clickable-only"
}
},
"label": "有限生成阿贝尔群",
"context": {
"range": [
36138,
37123
],
"quote": "这里 $(p_1p_0)$ 前面的 $-$ 应当理解为有限生成阿贝尔群意义下的负号。事实上，$(p_1p_0)$ 被看作 $(p_0p_1)$ 的逆元。从 $p_0$ 走到 $p_1$，再从 $p_1$ 走到 $p_0$，等于哪里也没去，即 $(p_0p_1) + (p_1p_0) = 0$，因此 $-(p_1p_0) = (p_0p_1)$。",
"quote_sha256": "d7eefb3d07f61827fe93c3ee6cb6df65db8a35bafe85f4e96d8b1142329b8078",
"environment": null,
"excerpt_omitted": false
},
"parallel_readings": [
{
"route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/03-section-3-3",
"lang": "en",
"source_category": "machine_draft",
"basis": "registered-book-edition-section-language-context; not-concept-equivalence"
}
],
"id": "occ-c8ffc1da619982dbf3d24310"
}
],
"registered_positions": [],
"statements": [],
"resolved_references": [
{
"raw": "href=\"03-section-3-3.md#bound-definition-1ccd5413f50b8ab807558a49\"",
"href": "03-section-3-3.md#bound-definition-1ccd5413f50b8ab807558a49",
"range": [
14259,
14325
],
"relation": "references",
"target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/03-section-3-3",
"target_anchor": "bound-definition-1ccd5413f50b8ab807558a49",
"resolved": true,
"reason": null,
"source_revision": "8c227052a7dbfe622e71625cd78cab83dfb97f5703f66636a4ca4fc6fc24676b",
"source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/01-section-3-1",
"occurrence_id": "occ-8d1b6bead38429222a6d2976"
}
],
"reading_order": [
"occ-8d1b6bead38429222a6d2976",
"occ-c8ffc1da619982dbf3d24310"
],
"recorded_dependencies": [],
"reading_paths": [],
"coverage": {
"registered_positions": 0,
"located_occurrences": 2,
"whole_book_search_complete": false,
"registered_positions_truncated": false,
"independent_human_review_implied": false
},
"unresolved": [],
"reviewed_definitions": [
{
"concept_id": "urn:uuid:fc4d4ed6-1e21-45ac-81f8-30621814489a",
"definition_id": "urn:uuid:f7b76454-3244-5356-9764-44f93c10b935",
"definition_group": null,
"path": "library/concepts/source-evidence/mcp/a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b.txt",
"range": [
0,
395
],
"quote": "form a subgroup of $G$ , which we denote $H$ . $H$ is called a subgroup of $G$ generated by the generators $x_{1},\\ldots ,x_{r}$ . If $G$ itself is generated by finite elements $x_{1},\\ldots ,x_{r}$ , $G$ is said to be finitely generated. If $n_1x_1 + \\dots +n_rx_r = 0$ is satisfied only when $n_1 = \\dots = n_r = 0$ , $x_{1},\\ldots ,x_{r}$ are said to be linearly independent.",
"document_sha256": "a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b",
"quote_sha256": "a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b",
"book_id": "nakahara-geometry-topology-physics",
"edition_id": "second-edition-local",
"scope": {
"book_id": "nakahara-geometry-topology-physics",
"edition_id": "second-edition-local",
"source_id": "nakahara-mineru-bd76b709"
},
"section": "3.1.2",
"pdf_page_index": 114,
"node": "a-e321b7fd2333bb9d6383e2e7",
"source_node_sha256": "a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b",
"upstream": {
"path": "library/concepts/source-evidence/mcp/9dfc3a878bc6ea51c6eb963738dff7073a61484280669689a853fb9f587c5eef.json",
"document_sha256": "9dfc3a878bc6ea51c6eb963738dff7073a61484280669689a853fb9f587c5eef",
"node_id": "a-e321b7fd2333bb9d6383e2e7",
"node_source_sha256": "a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b"
},
"conditions": "原书3.1.2中由有限多个元素整系数生成的阿贝尔群；与自由阿贝尔群及其结构定理不同。管理员核对的原书定义/陈述；不声明首次出现，不把Theorem环境伪作Definition编号。",
"review_status": "librarian-original-source-reviewed",
"source_locator": {
"path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/nakahara-3.yaml",
"sha256": "e2ce8c10e8b2dce6ebc05d605511f1bfd7a53799e562eb681ec7c2c381fa00c4",
"book_id": "nakahara-geometry-topology-physics",
"edition_id": "second-edition-local",
"nodes": [
"a-e321b7fd2333bb9d6383e2e7"
],
"node_hashes": {
"a-e321b7fd2333bb9d6383e2e7": "a0e513805fd048d838308f013755d36d1dc57acea5f1259b5cecb5e9de61209b"
}
},
"role": "definition",
"first_in_book": "not-established",
"evidence_origin": "explicit-reviewed-source-manifest",
"reading_links": [
{
"route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-03/01-section-3-1",
"anchor": "node-a-e321b7fd2333bb9d6383e2e7",
"lang": "en",
"basis": "explicit-source-anchor"
},
{
"route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-03/01-section-3-1",
"anchor": "node-a-e321b7fd2333bb9d6383e2e7",
"lang": "zh-CN",
"basis": "explicit-source-anchor"
}
]
}
],
"part_of_speech": "noun",
"base_revision": "224dbc22b31e75b19eb1fbb8892287deab0a7bf5eb914aa20ea438e2a373b5a8",
"optional_enrichments": []
}