{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZLJ2PJYKR7OLS2RZ6M5B3LESOT","short_pith_number":"pith:ZLJ2PJYK","schema_version":"1.0","canonical_sha256":"cad3a7a70a8fdcb96a39f33a1dac9274f5993a32e8c4b993b17aed5002585d41","source":{"kind":"arxiv","id":"1312.5991","version":4},"attestation_state":"computed","paper":{"title":"Metabelian associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"G. Militaru","submitted_at":"2013-12-20T15:35:38Z","abstract_excerpt":"Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \\in A$. We prove that the It\\^{o}'s theorem for groups remains valid for associative algebras. A structure theorem for metabelian algebras is given in terms of pure linear algebra tools and their classification from the view point of the extension problem is proven. Two border-line cases are worked out in detail: all metabelian algebras having the derived algebra of dimension $1$ "},"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":"1312.5991","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-20T15:35:38Z","cross_cats_sorted":[],"title_canon_sha256":"5e0c354f70a3281f490e3dbc0ddf109c15b2e7a8ba85bc69ff4dd56f99e1bf76","abstract_canon_sha256":"a099d7921594037f75d3d69600052c19f98814668c225c7b066fd6fdd45e24d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:08.009696Z","signature_b64":"P3dj7ijnW39BcIF5Nnh+ijlyWAQBTjlZahhYDVwLESxRx/2kpESBCGGOayCMRIyrdjqZTVw95Om1qZHH+ra/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cad3a7a70a8fdcb96a39f33a1dac9274f5993a32e8c4b993b17aed5002585d41","last_reissued_at":"2026-05-18T01:37:08.009050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:08.009050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metabelian associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"G. Militaru","submitted_at":"2013-12-20T15:35:38Z","abstract_excerpt":"Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \\in A$. We prove that the It\\^{o}'s theorem for groups remains valid for associative algebras. A structure theorem for metabelian algebras is given in terms of pure linear algebra tools and their classification from the view point of the extension problem is proven. Two border-line cases are worked out in detail: all metabelian algebras having the derived algebra of dimension $1$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5991","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":"1312.5991","created_at":"2026-05-18T01:37:08.009154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.5991v4","created_at":"2026-05-18T01:37:08.009154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5991","created_at":"2026-05-18T01:37:08.009154+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZLJ2PJYKR7OL","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZLJ2PJYKR7OLS2RZ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZLJ2PJYK","created_at":"2026-05-18T12:28:09.283467+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/ZLJ2PJYKR7OLS2RZ6M5B3LESOT","json":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT.json","graph_json":"https://pith.science/api/pith-number/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/graph.json","events_json":"https://pith.science/api/pith-number/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/events.json","paper":"https://pith.science/paper/ZLJ2PJYK"},"agent_actions":{"view_html":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT","download_json":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT.json","view_paper":"https://pith.science/paper/ZLJ2PJYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.5991&json=true","fetch_graph":"https://pith.science/api/pith-number/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/graph.json","fetch_events":"https://pith.science/api/pith-number/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/action/storage_attestation","attest_author":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/action/author_attestation","sign_citation":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/action/citation_signature","submit_replication":"https://pith.science/pith/ZLJ2PJYKR7OLS2RZ6M5B3LESOT/action/replication_record"}},"created_at":"2026-05-18T01:37:08.009154+00:00","updated_at":"2026-05-18T01:37:08.009154+00:00"}