{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DKHRY7BPWPOTSWKV66YL3OEA5G","short_pith_number":"pith:DKHRY7BP","schema_version":"1.0","canonical_sha256":"1a8f1c7c2fb3dd395955f7b0bdb880e9aa3c7cd58d506485925585a86c663e40","source":{"kind":"arxiv","id":"1812.04320","version":1},"attestation_state":"computed","paper":{"title":"Nilpotent elements control the structure of a module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Ssevviiri","submitted_at":"2018-12-11T10:36:26Z","abstract_excerpt":"A relationship between nilpotency and primeness in a module is investigated. Reduced modules are expressed as sums of prime modules. It is shown that presence of nilpotent module elements inhibits a module from possessing good structural properties.\n  A general form is given of an example used in literature to distinguish: 1) completely prime modules from prime modules, 2) classical prime modules from classical completely prime modules, and 3) a module which satisfies the complete radical formula from one which is neither 2-primal nor satisfies the radical formula."},"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":"1812.04320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-12-11T10:36:26Z","cross_cats_sorted":[],"title_canon_sha256":"118d82943ea692bfb3f1e405c28fb42873670672549c6c8c4f2a9a9cdcafc1de","abstract_canon_sha256":"c2a4d83d0f48ca0b9e309d977a182bac6bb56abed0dcc0ae22a0f9259cfe8fd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.559926Z","signature_b64":"duaJMUQ98yA+Kv3cxK4FDi4qmK1QzH35zE9GPghYLkpTdsJ/rkBqHQ7Nx9HJnkFd7GWfrhHm7IZpVfN/Y5CLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a8f1c7c2fb3dd395955f7b0bdb880e9aa3c7cd58d506485925585a86c663e40","last_reissued_at":"2026-05-17T23:58:32.559093Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.559093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nilpotent elements control the structure of a module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David Ssevviiri","submitted_at":"2018-12-11T10:36:26Z","abstract_excerpt":"A relationship between nilpotency and primeness in a module is investigated. Reduced modules are expressed as sums of prime modules. It is shown that presence of nilpotent module elements inhibits a module from possessing good structural properties.\n  A general form is given of an example used in literature to distinguish: 1) completely prime modules from prime modules, 2) classical prime modules from classical completely prime modules, and 3) a module which satisfies the complete radical formula from one which is neither 2-primal nor satisfies the radical formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04320","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":"1812.04320","created_at":"2026-05-17T23:58:32.559236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04320v1","created_at":"2026-05-17T23:58:32.559236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04320","created_at":"2026-05-17T23:58:32.559236+00:00"},{"alias_kind":"pith_short_12","alias_value":"DKHRY7BPWPOT","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DKHRY7BPWPOTSWKV","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DKHRY7BP","created_at":"2026-05-18T12:32:19.392346+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/DKHRY7BPWPOTSWKV66YL3OEA5G","json":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G.json","graph_json":"https://pith.science/api/pith-number/DKHRY7BPWPOTSWKV66YL3OEA5G/graph.json","events_json":"https://pith.science/api/pith-number/DKHRY7BPWPOTSWKV66YL3OEA5G/events.json","paper":"https://pith.science/paper/DKHRY7BP"},"agent_actions":{"view_html":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G","download_json":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G.json","view_paper":"https://pith.science/paper/DKHRY7BP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04320&json=true","fetch_graph":"https://pith.science/api/pith-number/DKHRY7BPWPOTSWKV66YL3OEA5G/graph.json","fetch_events":"https://pith.science/api/pith-number/DKHRY7BPWPOTSWKV66YL3OEA5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G/action/storage_attestation","attest_author":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G/action/author_attestation","sign_citation":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G/action/citation_signature","submit_replication":"https://pith.science/pith/DKHRY7BPWPOTSWKV66YL3OEA5G/action/replication_record"}},"created_at":"2026-05-17T23:58:32.559236+00:00","updated_at":"2026-05-17T23:58:32.559236+00:00"}