{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XGLX77LEHML4UWWSKI6MKVCRS7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf18aa276b9ed1d2e901fe471509455e93da37dad0e74c95d0bcffb029c1d962","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-09T18:48:22Z","title_canon_sha256":"cf53b229c2c5538d448c96ba81070d01c802c9b91e77cc667c48eaebaed9f184"},"schema_version":"1.0","source":{"id":"1705.03489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03489","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03489v1","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03489","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"XGLX77LEHML4","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XGLX77LEHML4UWWS","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XGLX77LE","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:36a687ddbb3e3c44941a050c2781d21f4c11b2ecd74585a01163aa64ec4280a8","target":"graph","created_at":"2026-05-18T00:44:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The formal study of completely prime modules was initiated by N. J. Groenewald and the current author in the paper; Completely prime submodules, {\\it Int. Elect. J. Algebra}, {\\bf 13}, (2013), 1--14. In this paper, the study of completely prime modules is continued. Firstly, the advantage completely prime modules have over prime modules is highlited and different situations that lead to completely prime modules given. Later, emphasis is put on fully completely prime modules, (i.e., modules whose all submodules are completely prime). For a fully completely prime left $R$-module $M$, if $a, b\\in","authors_text":"David Ssevviiri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-09T18:48:22Z","title":"On completely prime submodules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03489","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a5172330e0572aeb5f9f079e57940eef0bb5eca80b7e6af11f181b78d5e6b7dc","target":"record","created_at":"2026-05-18T00:44:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf18aa276b9ed1d2e901fe471509455e93da37dad0e74c95d0bcffb029c1d962","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-09T18:48:22Z","title_canon_sha256":"cf53b229c2c5538d448c96ba81070d01c802c9b91e77cc667c48eaebaed9f184"},"schema_version":"1.0","source":{"id":"1705.03489","kind":"arxiv","version":1}},"canonical_sha256":"b9977ffd643b17ca5ad2523cc5545197d7e39504f27851175674cde3059a11d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9977ffd643b17ca5ad2523cc5545197d7e39504f27851175674cde3059a11d2","first_computed_at":"2026-05-18T00:44:43.792282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:43.792282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"88VKM2D6ZOGhQDYZhmlbG5CuUodI5kdLvyFdJyiWvz9GspEmEyFCvk6Y3xmdStIuHYWnok4nHtnPgfGLCZYkDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:43.792897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5172330e0572aeb5f9f079e57940eef0bb5eca80b7e6af11f181b78d5e6b7dc","sha256:36a687ddbb3e3c44941a050c2781d21f4c11b2ecd74585a01163aa64ec4280a8"],"state_sha256":"eaba320e9c5015cfa95746141d6b3291d68a3569aa04881a0c5104d28f6210df"}