{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:J2JMXAGHZQSSEPQZB6KP6LFYIU","short_pith_number":"pith:J2JMXAGH","schema_version":"1.0","canonical_sha256":"4e92cb80c7cc25223e190f94ff2cb8450c42fae4afaff2690818892d3fa5a3aa","source":{"kind":"arxiv","id":"1308.3459","version":4},"attestation_state":"computed","paper":{"title":"Simple Semigroup Graded Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Nystedt","submitted_at":"2013-08-15T17:11:13Z","abstract_excerpt":"We show that if $R$ is a, not necessarily unital, ring graded by a semigroup $G$ equipped with an idempotent $e$ such that $G$ is cancellative at $e$, the non-zero elements of $eGe$ form a hypercentral group and $R_e$ has a non-zero idempotent $f$, then $R$ is simple if and only if it is graded simple and the center of the corner subring $f R_{eGe} f$ is a field. This is a generalization of a result of E. Jespers' on the simplicity of a unital ring graded by a hypercentral group. We apply our result to partial skew group rings and obtain necessary and sufficient conditions for the simplicity o"},"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":"1308.3459","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-15T17:11:13Z","cross_cats_sorted":[],"title_canon_sha256":"42b05309b9eac324eb75f91e8cda9a7d2f7e4339d68f6677bd9226966f3e95bf","abstract_canon_sha256":"ae4648afbc7c9fe0dc655a4203683904cf0b3c9b762993c4d336a88aa1047aa9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:16.483878Z","signature_b64":"G5ftfS9/FjmlOnNa3Njcm/f5XO/Jl5bxilR4BTFt09Bgq9LOBNSCvaU2bgZP5L6GNpuVLOy6DvswbOTI1CFwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e92cb80c7cc25223e190f94ff2cb8450c42fae4afaff2690818892d3fa5a3aa","last_reissued_at":"2026-05-18T02:43:16.483309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:16.483309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple Semigroup Graded Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Johan \\\"Oinert, Patrik Nystedt","submitted_at":"2013-08-15T17:11:13Z","abstract_excerpt":"We show that if $R$ is a, not necessarily unital, ring graded by a semigroup $G$ equipped with an idempotent $e$ such that $G$ is cancellative at $e$, the non-zero elements of $eGe$ form a hypercentral group and $R_e$ has a non-zero idempotent $f$, then $R$ is simple if and only if it is graded simple and the center of the corner subring $f R_{eGe} f$ is a field. This is a generalization of a result of E. Jespers' on the simplicity of a unital ring graded by a hypercentral group. We apply our result to partial skew group rings and obtain necessary and sufficient conditions for the simplicity o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3459","kind":"arxiv","version":4},"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":"1308.3459","created_at":"2026-05-18T02:43:16.483407+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.3459v4","created_at":"2026-05-18T02:43:16.483407+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3459","created_at":"2026-05-18T02:43:16.483407+00:00"},{"alias_kind":"pith_short_12","alias_value":"J2JMXAGHZQSS","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"J2JMXAGHZQSSEPQZ","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"J2JMXAGH","created_at":"2026-05-18T12:27:49.015174+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/J2JMXAGHZQSSEPQZB6KP6LFYIU","json":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU.json","graph_json":"https://pith.science/api/pith-number/J2JMXAGHZQSSEPQZB6KP6LFYIU/graph.json","events_json":"https://pith.science/api/pith-number/J2JMXAGHZQSSEPQZB6KP6LFYIU/events.json","paper":"https://pith.science/paper/J2JMXAGH"},"agent_actions":{"view_html":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU","download_json":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU.json","view_paper":"https://pith.science/paper/J2JMXAGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.3459&json=true","fetch_graph":"https://pith.science/api/pith-number/J2JMXAGHZQSSEPQZB6KP6LFYIU/graph.json","fetch_events":"https://pith.science/api/pith-number/J2JMXAGHZQSSEPQZB6KP6LFYIU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU/action/storage_attestation","attest_author":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU/action/author_attestation","sign_citation":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU/action/citation_signature","submit_replication":"https://pith.science/pith/J2JMXAGHZQSSEPQZB6KP6LFYIU/action/replication_record"}},"created_at":"2026-05-18T02:43:16.483407+00:00","updated_at":"2026-05-18T02:43:16.483407+00:00"}