{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:75NCS6DSL3CSEO2QO2N7P76UKC","short_pith_number":"pith:75NCS6DS","schema_version":"1.0","canonical_sha256":"ff5a2978725ec5223b50769bf7ffd450b513efb905a025fe0e560503329f3a99","source":{"kind":"arxiv","id":"1103.5020","version":2},"attestation_state":"computed","paper":{"title":"D\\'ecomposition effective de Jordan-Chevalley et ses retomb\\'ees en enseignement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Danielle Couty (IMT), Jean Esterle (IMB), Rachid Zarouf (LATP)","submitted_at":"2011-03-25T16:32:04Z","abstract_excerpt":"The purpose of this paper is to point the effectiveness of the Jordan-Chevalley decomposition, i.e. the decomposition of a square matrix $U$ with coefficients in a field $k$ containing the eigenvalues of $U$ as a sum $U=D+N,$ where $D$ is a diagonalizable matrix and $N$ a nilpotent matrix which commutes with $D.$ The most general version of this decomposition shows that every separable element $u$ of a $k$-algebra $A$ can be written in a unique way as a sum $u=d+n,$ where $d \\in A$ is absolutely semi-simple and where $n\\in A$ is nilpotent and commutes with $d.$ In fact an algorithm, due to C. "},"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":"1103.5020","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-03-25T16:32:04Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"ec61d85db959b1296a92337ca6ba0f5546eeab3ec4faa7769a3ca0f6647e3677","abstract_canon_sha256":"724a163248392f5ce5d5365e99fd522a680ba2107c5e93c0fe7264b646ba473c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.128122Z","signature_b64":"FinUjxUOk4btFiV35h+gJU9sBAcx9eEuuStVIu9qNOeTYQZ4u80XKYk/oloXmXnvU6n2KU9T/y0SoJW4xia6Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff5a2978725ec5223b50769bf7ffd450b513efb905a025fe0e560503329f3a99","last_reissued_at":"2026-05-18T03:36:27.127606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.127606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"D\\'ecomposition effective de Jordan-Chevalley et ses retomb\\'ees en enseignement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Danielle Couty (IMT), Jean Esterle (IMB), Rachid Zarouf (LATP)","submitted_at":"2011-03-25T16:32:04Z","abstract_excerpt":"The purpose of this paper is to point the effectiveness of the Jordan-Chevalley decomposition, i.e. the decomposition of a square matrix $U$ with coefficients in a field $k$ containing the eigenvalues of $U$ as a sum $U=D+N,$ where $D$ is a diagonalizable matrix and $N$ a nilpotent matrix which commutes with $D.$ The most general version of this decomposition shows that every separable element $u$ of a $k$-algebra $A$ can be written in a unique way as a sum $u=d+n,$ where $d \\in A$ is absolutely semi-simple and where $n\\in A$ is nilpotent and commutes with $d.$ In fact an algorithm, due to C. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5020","kind":"arxiv","version":2},"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":"1103.5020","created_at":"2026-05-18T03:36:27.127671+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.5020v2","created_at":"2026-05-18T03:36:27.127671+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.5020","created_at":"2026-05-18T03:36:27.127671+00:00"},{"alias_kind":"pith_short_12","alias_value":"75NCS6DSL3CS","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"75NCS6DSL3CSEO2Q","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"75NCS6DS","created_at":"2026-05-18T12:26:22.705136+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/75NCS6DSL3CSEO2QO2N7P76UKC","json":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC.json","graph_json":"https://pith.science/api/pith-number/75NCS6DSL3CSEO2QO2N7P76UKC/graph.json","events_json":"https://pith.science/api/pith-number/75NCS6DSL3CSEO2QO2N7P76UKC/events.json","paper":"https://pith.science/paper/75NCS6DS"},"agent_actions":{"view_html":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC","download_json":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC.json","view_paper":"https://pith.science/paper/75NCS6DS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.5020&json=true","fetch_graph":"https://pith.science/api/pith-number/75NCS6DSL3CSEO2QO2N7P76UKC/graph.json","fetch_events":"https://pith.science/api/pith-number/75NCS6DSL3CSEO2QO2N7P76UKC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC/action/storage_attestation","attest_author":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC/action/author_attestation","sign_citation":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC/action/citation_signature","submit_replication":"https://pith.science/pith/75NCS6DSL3CSEO2QO2N7P76UKC/action/replication_record"}},"created_at":"2026-05-18T03:36:27.127671+00:00","updated_at":"2026-05-18T03:36:27.127671+00:00"}