{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:5TXBFVGXCYAOT4BOFEE2Q33OXT","short_pith_number":"pith:5TXBFVGX","schema_version":"1.0","canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","source":{"kind":"arxiv","id":"1810.01282","version":1},"attestation_state":"computed","paper":{"title":"Weak Nil Clean Ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ajay Sharma, Dhiren Kumar Basnet","submitted_at":"2018-10-01T05:45:12Z","abstract_excerpt":"As a generalization of nil clean ideal, we define weak nil clean ideal of a ring. An ideal $I$ of a ring $R$ is weak nil clean ideal if for any $x\\in I$, either $x=e+n$ or $x=-e+n$, where $n$ is a nilpotent element and $e$ is an idempotent element of $R$. Some interesting properties of weak nil clean ideal and its relation with weak nil clean ring have been discussed."},"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":"1810.01282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-10-01T05:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"874603511288840cd26cbcc8de80e1d887c6af1521776f2d457b8fd1dabf35a1","abstract_canon_sha256":"4af92b0fd577627e3b90c1014e365b8c25ab3189592dc4086ef7f90bef33c193"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:18.350567Z","signature_b64":"4PwEgEE5FVftF5SY2o1TgX34m5fqVxDIoHj8RLK5jreyNBp8busc0LLuOihjKNwc1lVAFlXiG1mjtx/5e/gcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecee12d4d71600e9f02e2909a86f6ebccdba7f64fe221bdbdcf40c70235e32a6","last_reissued_at":"2026-05-18T00:04:18.349746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:18.349746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Nil Clean Ideal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ajay Sharma, Dhiren Kumar Basnet","submitted_at":"2018-10-01T05:45:12Z","abstract_excerpt":"As a generalization of nil clean ideal, we define weak nil clean ideal of a ring. An ideal $I$ of a ring $R$ is weak nil clean ideal if for any $x\\in I$, either $x=e+n$ or $x=-e+n$, where $n$ is a nilpotent element and $e$ is an idempotent element of $R$. Some interesting properties of weak nil clean ideal and its relation with weak nil clean ring have been discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01282","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":"1810.01282","created_at":"2026-05-18T00:04:18.349848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01282v1","created_at":"2026-05-18T00:04:18.349848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01282","created_at":"2026-05-18T00:04:18.349848+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TXBFVGXCYAO","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TXBFVGXCYAOT4BO","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TXBFVGX","created_at":"2026-05-18T12:32:08.215937+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/5TXBFVGXCYAOT4BOFEE2Q33OXT","json":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT.json","graph_json":"https://pith.science/api/pith-number/5TXBFVGXCYAOT4BOFEE2Q33OXT/graph.json","events_json":"https://pith.science/api/pith-number/5TXBFVGXCYAOT4BOFEE2Q33OXT/events.json","paper":"https://pith.science/paper/5TXBFVGX"},"agent_actions":{"view_html":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT","download_json":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT.json","view_paper":"https://pith.science/paper/5TXBFVGX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01282&json=true","fetch_graph":"https://pith.science/api/pith-number/5TXBFVGXCYAOT4BOFEE2Q33OXT/graph.json","fetch_events":"https://pith.science/api/pith-number/5TXBFVGXCYAOT4BOFEE2Q33OXT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/action/storage_attestation","attest_author":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/action/author_attestation","sign_citation":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/action/citation_signature","submit_replication":"https://pith.science/pith/5TXBFVGXCYAOT4BOFEE2Q33OXT/action/replication_record"}},"created_at":"2026-05-18T00:04:18.349848+00:00","updated_at":"2026-05-18T00:04:18.349848+00:00"}