{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:K62F7RF2K45WF3EPP4KXLZPWVO","short_pith_number":"pith:K62F7RF2","schema_version":"1.0","canonical_sha256":"57b45fc4ba573b62ec8f7f1575e5f6ab9ed45d3fbc9df4d26becef736c3fe77a","source":{"kind":"arxiv","id":"1503.00308","version":1},"attestation_state":"computed","paper":{"title":"On 2-absorbing primary submodules of modules over commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmad Yousefian Darani, Ece Yetkin, Hojjat Mostafanasab, \\\"Unsal Tekir","submitted_at":"2015-03-01T17:00:10Z","abstract_excerpt":"All rings are commutative with $1\\neq0$, and all modules are unital. The purpose of this paper is to investigate the concept of $2$-absorbing primary submodules generalizing $2$-absorbing primary ideals of rings. Let $M$ be an $R$-module. A proper submodule $N$ of an $R$-module $M$ is called a $2$-absorbing primary submodule of $M$ if whenever $a,b\\in R$ and $m\\in M$ and $abm\\in N$, then $am\\in M$-$rad(N)$ or $bm\\in M$-$rad(N)$ or $ab\\in(N:_RM)$. It is shown that a proper submodule $N$ of $M$ is a $2$-absorbing primary submodule if and only if whenever $I_1I_2K\\subseteq N$ for some ideals $I_1"},"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":"1503.00308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-03-01T17:00:10Z","cross_cats_sorted":[],"title_canon_sha256":"b8b785fbd93df141c1783ddbc301402463f9fe34ef0341b0ce0de6d32f3584d4","abstract_canon_sha256":"d8ab5c9332ceae1780c7eb6bb0d0d5ffda7547c8a8d2e88f779d0b9b610143bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:54.709171Z","signature_b64":"ZQJV9nTSEyjyqQAp47biYK1iP1pXfHoyFbjVPs4mKBl0JZ/9BButYONeWq7vPXTbOf2eek4h+4gcI6SfUDm4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57b45fc4ba573b62ec8f7f1575e5f6ab9ed45d3fbc9df4d26becef736c3fe77a","last_reissued_at":"2026-05-18T02:25:54.708764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:54.708764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 2-absorbing primary submodules of modules over commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmad Yousefian Darani, Ece Yetkin, Hojjat Mostafanasab, \\\"Unsal Tekir","submitted_at":"2015-03-01T17:00:10Z","abstract_excerpt":"All rings are commutative with $1\\neq0$, and all modules are unital. The purpose of this paper is to investigate the concept of $2$-absorbing primary submodules generalizing $2$-absorbing primary ideals of rings. Let $M$ be an $R$-module. A proper submodule $N$ of an $R$-module $M$ is called a $2$-absorbing primary submodule of $M$ if whenever $a,b\\in R$ and $m\\in M$ and $abm\\in N$, then $am\\in M$-$rad(N)$ or $bm\\in M$-$rad(N)$ or $ab\\in(N:_RM)$. It is shown that a proper submodule $N$ of $M$ is a $2$-absorbing primary submodule if and only if whenever $I_1I_2K\\subseteq N$ for some ideals $I_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00308","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":"1503.00308","created_at":"2026-05-18T02:25:54.708831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00308v1","created_at":"2026-05-18T02:25:54.708831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00308","created_at":"2026-05-18T02:25:54.708831+00:00"},{"alias_kind":"pith_short_12","alias_value":"K62F7RF2K45W","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"K62F7RF2K45WF3EP","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"K62F7RF2","created_at":"2026-05-18T12:29:27.538025+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/K62F7RF2K45WF3EPP4KXLZPWVO","json":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO.json","graph_json":"https://pith.science/api/pith-number/K62F7RF2K45WF3EPP4KXLZPWVO/graph.json","events_json":"https://pith.science/api/pith-number/K62F7RF2K45WF3EPP4KXLZPWVO/events.json","paper":"https://pith.science/paper/K62F7RF2"},"agent_actions":{"view_html":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO","download_json":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO.json","view_paper":"https://pith.science/paper/K62F7RF2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00308&json=true","fetch_graph":"https://pith.science/api/pith-number/K62F7RF2K45WF3EPP4KXLZPWVO/graph.json","fetch_events":"https://pith.science/api/pith-number/K62F7RF2K45WF3EPP4KXLZPWVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO/action/storage_attestation","attest_author":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO/action/author_attestation","sign_citation":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO/action/citation_signature","submit_replication":"https://pith.science/pith/K62F7RF2K45WF3EPP4KXLZPWVO/action/replication_record"}},"created_at":"2026-05-18T02:25:54.708831+00:00","updated_at":"2026-05-18T02:25:54.708831+00:00"}