{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QA34VXPKMMCKSTRLFONZGFK2ZF","short_pith_number":"pith:QA34VXPK","schema_version":"1.0","canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","source":{"kind":"arxiv","id":"1812.02456","version":1},"attestation_state":"computed","paper":{"title":"Quasi-prime ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Abolfazl Tarizadeh, Mohsen Aghajani","submitted_at":"2018-12-06T10:57:46Z","abstract_excerpt":"In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which generalizes the Zariski topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum"},"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":"1812.02456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"ca42356555ff252c7e45d5da47de3d73dbd661c3294632fe9c18053fc9f0f5b1","abstract_canon_sha256":"747716a764e289c68bc56b1f2b8f00357e9356c3769481672b76ab6fd986e5d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.650985Z","signature_b64":"QQ+1fA84wOnh9rwzk8Tf+5EkgEYRIj72k2RuRU8B3KycwL6o4UYfrp16Jf/NHBoNHhpCIEYnli0xMBeEdpYqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","last_reissued_at":"2026-05-17T23:58:55.650515Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.650515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-prime ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Abolfazl Tarizadeh, Mohsen Aghajani","submitted_at":"2018-12-06T10:57:46Z","abstract_excerpt":"In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which generalizes the Zariski topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02456","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":"1812.02456","created_at":"2026-05-17T23:58:55.650600+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.02456v1","created_at":"2026-05-17T23:58:55.650600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02456","created_at":"2026-05-17T23:58:55.650600+00:00"},{"alias_kind":"pith_short_12","alias_value":"QA34VXPKMMCK","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QA34VXPKMMCKSTRL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QA34VXPK","created_at":"2026-05-18T12:32:46.962924+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/QA34VXPKMMCKSTRLFONZGFK2ZF","json":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF.json","graph_json":"https://pith.science/api/pith-number/QA34VXPKMMCKSTRLFONZGFK2ZF/graph.json","events_json":"https://pith.science/api/pith-number/QA34VXPKMMCKSTRLFONZGFK2ZF/events.json","paper":"https://pith.science/paper/QA34VXPK"},"agent_actions":{"view_html":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF","download_json":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF.json","view_paper":"https://pith.science/paper/QA34VXPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.02456&json=true","fetch_graph":"https://pith.science/api/pith-number/QA34VXPKMMCKSTRLFONZGFK2ZF/graph.json","fetch_events":"https://pith.science/api/pith-number/QA34VXPKMMCKSTRLFONZGFK2ZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/action/storage_attestation","attest_author":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/action/author_attestation","sign_citation":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/action/citation_signature","submit_replication":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/action/replication_record"}},"created_at":"2026-05-17T23:58:55.650600+00:00","updated_at":"2026-05-17T23:58:55.650600+00:00"}