{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2WKMYF4HDVTGMOZD4RHUSBTTRL","short_pith_number":"pith:2WKMYF4H","schema_version":"1.0","canonical_sha256":"d594cc17871d66663b23e44f4906738af27e8745d1abed6f5fa5ccc331c3e798","source":{"kind":"arxiv","id":"1109.5062","version":1},"attestation_state":"computed","paper":{"title":"Invertible unital bimodules over rings with local units, and related exact sequences of groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"J. G\\'omez-Torrecillas, L. El Kaoutit","submitted_at":"2011-09-23T13:01:30Z","abstract_excerpt":"Let $R$ be a ring with a set of local units, and a homomorphism of groups $\\underline{\\Theta} : \\G \\to \\Picar{R}$ to the Picard group of $R$. We study under which conditions $\\underline{\\Theta}$ is determined by a factor map, and, henceforth, it defines a generalized crossed product with a same set of local units. Given a ring extension $R \\subseteq S$ with the same set of local units and assuming that $\\underline{\\Theta}$ is induced by a homomorphism of groups $\\G \\to \\Inv{R}{S}$ to the group of all invertible $R$-sub-bimodules of $S$, then we construct an analogue of the Chase-Harrison-Rosen"},"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":"1109.5062","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-09-23T13:01:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"192b4a629a12e0720cee8ca84c4bef0b2de9d2dbeeaf86d712f26583d637c0cc","abstract_canon_sha256":"b06bd088fae7dcea8786e304788cf68feaf03dab89a8d5a03dcfea230ae1ae53"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:21.857754Z","signature_b64":"2C9px67urOpaLPMoy3YDHJ567tna/TkiIEKuiLiQWJbtgFjjnNiEuqYK3HX9WvQwtNWyOqRlyQEAkFGKXbLACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d594cc17871d66663b23e44f4906738af27e8745d1abed6f5fa5ccc331c3e798","last_reissued_at":"2026-05-18T04:12:21.857021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:21.857021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invertible unital bimodules over rings with local units, and related exact sequences of groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.RA","authors_text":"J. G\\'omez-Torrecillas, L. El Kaoutit","submitted_at":"2011-09-23T13:01:30Z","abstract_excerpt":"Let $R$ be a ring with a set of local units, and a homomorphism of groups $\\underline{\\Theta} : \\G \\to \\Picar{R}$ to the Picard group of $R$. We study under which conditions $\\underline{\\Theta}$ is determined by a factor map, and, henceforth, it defines a generalized crossed product with a same set of local units. Given a ring extension $R \\subseteq S$ with the same set of local units and assuming that $\\underline{\\Theta}$ is induced by a homomorphism of groups $\\G \\to \\Inv{R}{S}$ to the group of all invertible $R$-sub-bimodules of $S$, then we construct an analogue of the Chase-Harrison-Rosen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5062","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":"1109.5062","created_at":"2026-05-18T04:12:21.857134+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.5062v1","created_at":"2026-05-18T04:12:21.857134+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5062","created_at":"2026-05-18T04:12:21.857134+00:00"},{"alias_kind":"pith_short_12","alias_value":"2WKMYF4HDVTG","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2WKMYF4HDVTGMOZD","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2WKMYF4H","created_at":"2026-05-18T12:26:18.847500+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/2WKMYF4HDVTGMOZD4RHUSBTTRL","json":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL.json","graph_json":"https://pith.science/api/pith-number/2WKMYF4HDVTGMOZD4RHUSBTTRL/graph.json","events_json":"https://pith.science/api/pith-number/2WKMYF4HDVTGMOZD4RHUSBTTRL/events.json","paper":"https://pith.science/paper/2WKMYF4H"},"agent_actions":{"view_html":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL","download_json":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL.json","view_paper":"https://pith.science/paper/2WKMYF4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.5062&json=true","fetch_graph":"https://pith.science/api/pith-number/2WKMYF4HDVTGMOZD4RHUSBTTRL/graph.json","fetch_events":"https://pith.science/api/pith-number/2WKMYF4HDVTGMOZD4RHUSBTTRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL/action/storage_attestation","attest_author":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL/action/author_attestation","sign_citation":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL/action/citation_signature","submit_replication":"https://pith.science/pith/2WKMYF4HDVTGMOZD4RHUSBTTRL/action/replication_record"}},"created_at":"2026-05-18T04:12:21.857134+00:00","updated_at":"2026-05-18T04:12:21.857134+00:00"}