{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OTX6QI2USVQMTNWGBDVAKPNEBU","short_pith_number":"pith:OTX6QI2U","schema_version":"1.0","canonical_sha256":"74efe823549560c9b6c608ea053da40d2dbbabc1803da94b6f76cf297eb49063","source":{"kind":"arxiv","id":"1306.3141","version":1},"attestation_state":"computed","paper":{"title":"Idempotent generated algebras and Boolean powers of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.RA","authors_text":"Bruce Olberding, Guram Bezhanishvili, Patrick J. Morandi, Vincenzo Marra","submitted_at":"2013-06-13T15:35:16Z","abstract_excerpt":"A Boolean power S of a commutative ring R has the structure of a commutative R-algebra, and with respect to this structure, each element of S can be written uniquely as an R-linear combination of orthogonal idempotents so that the sum of the idempotents is 1 and their coefficients are distinct. In order to formalize this decomposition property, we introduce the concept of a Specker R-algebra, and we prove that the Boolean powers of R are up to isomorphism precisely the Specker R-algebras. We also show that these algebras are characterized in terms of a functorial construction having roots in t"},"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":"1306.3141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-06-13T15:35:16Z","cross_cats_sorted":["math.GN","math.LO"],"title_canon_sha256":"3037d99fed6ad475ff83a63394745dd18cb4b3e79ea4583c6c533a9183c39369","abstract_canon_sha256":"4984b4d78ab7f8079b39f861f4d22e3e92ee7b55daba0b0b1ae6b9daefc62c4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:59.490181Z","signature_b64":"ok+/kRAuYlw40MfVnoe8s7eMskD3XtIO2R78gQUbI2FfnAQx0tjLg5zeJ56FGLkq6yP5Rcc0k/EoYW4BVyptDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74efe823549560c9b6c608ea053da40d2dbbabc1803da94b6f76cf297eb49063","last_reissued_at":"2026-05-18T03:20:59.489673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:59.489673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Idempotent generated algebras and Boolean powers of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.LO"],"primary_cat":"math.RA","authors_text":"Bruce Olberding, Guram Bezhanishvili, Patrick J. Morandi, Vincenzo Marra","submitted_at":"2013-06-13T15:35:16Z","abstract_excerpt":"A Boolean power S of a commutative ring R has the structure of a commutative R-algebra, and with respect to this structure, each element of S can be written uniquely as an R-linear combination of orthogonal idempotents so that the sum of the idempotents is 1 and their coefficients are distinct. In order to formalize this decomposition property, we introduce the concept of a Specker R-algebra, and we prove that the Boolean powers of R are up to isomorphism precisely the Specker R-algebras. We also show that these algebras are characterized in terms of a functorial construction having roots in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3141","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":"1306.3141","created_at":"2026-05-18T03:20:59.489753+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.3141v1","created_at":"2026-05-18T03:20:59.489753+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3141","created_at":"2026-05-18T03:20:59.489753+00:00"},{"alias_kind":"pith_short_12","alias_value":"OTX6QI2USVQM","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OTX6QI2USVQMTNWG","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OTX6QI2U","created_at":"2026-05-18T12:27:54.935989+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/OTX6QI2USVQMTNWGBDVAKPNEBU","json":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU.json","graph_json":"https://pith.science/api/pith-number/OTX6QI2USVQMTNWGBDVAKPNEBU/graph.json","events_json":"https://pith.science/api/pith-number/OTX6QI2USVQMTNWGBDVAKPNEBU/events.json","paper":"https://pith.science/paper/OTX6QI2U"},"agent_actions":{"view_html":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU","download_json":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU.json","view_paper":"https://pith.science/paper/OTX6QI2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.3141&json=true","fetch_graph":"https://pith.science/api/pith-number/OTX6QI2USVQMTNWGBDVAKPNEBU/graph.json","fetch_events":"https://pith.science/api/pith-number/OTX6QI2USVQMTNWGBDVAKPNEBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU/action/storage_attestation","attest_author":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU/action/author_attestation","sign_citation":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU/action/citation_signature","submit_replication":"https://pith.science/pith/OTX6QI2USVQMTNWGBDVAKPNEBU/action/replication_record"}},"created_at":"2026-05-18T03:20:59.489753+00:00","updated_at":"2026-05-18T03:20:59.489753+00:00"}