{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4WRWHAR2X4TJVKF7B6TTPKPPMP","short_pith_number":"pith:4WRWHAR2","schema_version":"1.0","canonical_sha256":"e5a363823abf269aa8bf0fa737a9ef63f5b96e0c2cc84d0f43bb0813ef5d6890","source":{"kind":"arxiv","id":"1609.04052","version":1},"attestation_state":"computed","paper":{"title":"On classes of C3 and D3 modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abyzov Adel Nailevich, Tran Hoai Ngoc Nhan, Truong Cong Quynh","submitted_at":"2016-09-13T21:07:29Z","abstract_excerpt":"The aim of this paper is to study the notions of $\\mathcal{A}$-C3 and $\\mathcal{A}$-D3 modules for some class $\\mathcal{A}$ of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right $R$-module $F$ is a $V$-module if and only if every $F$-cyclic module $M$ is an $\\mathcal{A}$-C3 module where $\\mathcal{A}$ is the class of all simple submodules of $M$. Moreover, let $R$ be a right artinian ring and $\\mathcal{A}$, a class of right $R$-modules with local endomorphisms, containing all simp"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.04052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-13T21:07:29Z","cross_cats_sorted":[],"title_canon_sha256":"5ef1021f9fe8ce928be4ece4ef710349635a88e6b1960896b17078c85bc424bb","abstract_canon_sha256":"a9c7efe48d387d02f85abe3298d0892cf31689725abc0794e5b7bd6c270a754f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:40.803235Z","signature_b64":"U40C9I/rbcSYLeoICBz+Vcxz+00NcfJTNeWc5lTVrJEuGXemsyeSN+hQTFaXWKbGMypjl4mqgQ+9lGFhJQ+BBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a363823abf269aa8bf0fa737a9ef63f5b96e0c2cc84d0f43bb0813ef5d6890","last_reissued_at":"2026-05-18T01:04:40.802633Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:40.802633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On classes of C3 and D3 modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abyzov Adel Nailevich, Tran Hoai Ngoc Nhan, Truong Cong Quynh","submitted_at":"2016-09-13T21:07:29Z","abstract_excerpt":"The aim of this paper is to study the notions of $\\mathcal{A}$-C3 and $\\mathcal{A}$-D3 modules for some class $\\mathcal{A}$ of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right $R$-module $F$ is a $V$-module if and only if every $F$-cyclic module $M$ is an $\\mathcal{A}$-C3 module where $\\mathcal{A}$ is the class of all simple submodules of $M$. Moreover, let $R$ be a right artinian ring and $\\mathcal{A}$, a class of right $R$-modules with local endomorphisms, containing all simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04052","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.04052","created_at":"2026-05-18T01:04:40.802727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04052v1","created_at":"2026-05-18T01:04:40.802727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04052","created_at":"2026-05-18T01:04:40.802727+00:00"},{"alias_kind":"pith_short_12","alias_value":"4WRWHAR2X4TJ","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4WRWHAR2X4TJVKF7","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4WRWHAR2","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP","json":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP.json","graph_json":"https://pith.science/api/pith-number/4WRWHAR2X4TJVKF7B6TTPKPPMP/graph.json","events_json":"https://pith.science/api/pith-number/4WRWHAR2X4TJVKF7B6TTPKPPMP/events.json","paper":"https://pith.science/paper/4WRWHAR2"},"agent_actions":{"view_html":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP","download_json":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP.json","view_paper":"https://pith.science/paper/4WRWHAR2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04052&json=true","fetch_graph":"https://pith.science/api/pith-number/4WRWHAR2X4TJVKF7B6TTPKPPMP/graph.json","fetch_events":"https://pith.science/api/pith-number/4WRWHAR2X4TJVKF7B6TTPKPPMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP/action/storage_attestation","attest_author":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP/action/author_attestation","sign_citation":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP/action/citation_signature","submit_replication":"https://pith.science/pith/4WRWHAR2X4TJVKF7B6TTPKPPMP/action/replication_record"}},"created_at":"2026-05-18T01:04:40.802727+00:00","updated_at":"2026-05-18T01:04:40.802727+00:00"}