{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5EDONIBNHLBARPQ2PFBKC5NRNZ","short_pith_number":"pith:5EDONIBN","schema_version":"1.0","canonical_sha256":"e906e6a02d3ac208be1a7942a175b16e5deb9b83727e6b1d0bb0af1b6c98ffdd","source":{"kind":"arxiv","id":"1107.0447","version":1},"attestation_state":"computed","paper":{"title":"On $p-$Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mohammed Kabbour","submitted_at":"2011-07-03T11:33:14Z","abstract_excerpt":"In this paper, we introduced the concept of a $p$-ideal for a given ring. We provide necessary and sufficient condition for $\\dfrac{R[x]}{(f(x))}$ to be a $p$-ring, where $R$ is a finite $p$-ring. It is also shown that the amalgamation of rings, $A\\bowtie^fJ$ is a $p$-ring if and only if so is $A$ and $J$ is a $p$-ideal. Finally, we establish the transfer of this notion to trivial ring extensions."},"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":"1107.0447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-03T11:33:14Z","cross_cats_sorted":[],"title_canon_sha256":"1aac516c044e0d3a8fad9cc8b05fe10dbe0adaff12905455c7ab28c1f39a61e7","abstract_canon_sha256":"da8a9b8c556da936ed86602243e9a8ddfcc8a8daf38caf6a8065ebe35d6df3df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:53.949509Z","signature_b64":"2zJ44v8Pu0mFs240zYthMpak/kakAHKd2PtZe5yUXWH8y8oSCiMEPpWASJZHL5k1eJ7DOxkMdZkk3GFmzKDjBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e906e6a02d3ac208be1a7942a175b16e5deb9b83727e6b1d0bb0af1b6c98ffdd","last_reissued_at":"2026-05-18T04:18:53.949018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:53.949018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $p-$Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mohammed Kabbour","submitted_at":"2011-07-03T11:33:14Z","abstract_excerpt":"In this paper, we introduced the concept of a $p$-ideal for a given ring. We provide necessary and sufficient condition for $\\dfrac{R[x]}{(f(x))}$ to be a $p$-ring, where $R$ is a finite $p$-ring. It is also shown that the amalgamation of rings, $A\\bowtie^fJ$ is a $p$-ring if and only if so is $A$ and $J$ is a $p$-ideal. Finally, we establish the transfer of this notion to trivial ring extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0447","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":"1107.0447","created_at":"2026-05-18T04:18:53.949085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1107.0447v1","created_at":"2026-05-18T04:18:53.949085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0447","created_at":"2026-05-18T04:18:53.949085+00:00"},{"alias_kind":"pith_short_12","alias_value":"5EDONIBNHLBA","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5EDONIBNHLBARPQ2","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5EDONIBN","created_at":"2026-05-18T12:26:20.644004+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/5EDONIBNHLBARPQ2PFBKC5NRNZ","json":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ.json","graph_json":"https://pith.science/api/pith-number/5EDONIBNHLBARPQ2PFBKC5NRNZ/graph.json","events_json":"https://pith.science/api/pith-number/5EDONIBNHLBARPQ2PFBKC5NRNZ/events.json","paper":"https://pith.science/paper/5EDONIBN"},"agent_actions":{"view_html":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ","download_json":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ.json","view_paper":"https://pith.science/paper/5EDONIBN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1107.0447&json=true","fetch_graph":"https://pith.science/api/pith-number/5EDONIBNHLBARPQ2PFBKC5NRNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/5EDONIBNHLBARPQ2PFBKC5NRNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ/action/storage_attestation","attest_author":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ/action/author_attestation","sign_citation":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ/action/citation_signature","submit_replication":"https://pith.science/pith/5EDONIBNHLBARPQ2PFBKC5NRNZ/action/replication_record"}},"created_at":"2026-05-18T04:18:53.949085+00:00","updated_at":"2026-05-18T04:18:53.949085+00:00"}