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By Zorn's Lemma every non-Lie nilpotent variety contains a minimal such variety, called {\\em almost Lie nilpotent}, as a subvariety. A description of almost Lie nilpotent varieties for algebras over a field of characteristic 0 was made up by Yu.Mal'cev. We find a list of non-pri"},"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":"1108.5670","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-29T17:51:31Z","cross_cats_sorted":[],"title_canon_sha256":"d0d08ad851b59bc11f780d98069ad46f109891cf16af7ab0a38e9005183d30ee","abstract_canon_sha256":"65a69b5a4dc75849f6c94bac9d295f3d835e12d6f68fe1516390b3f99d6c6b60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:58.579935Z","signature_b64":"FJnLQVy1bTK7dOexIi+AiMZwTohDAS9UIZD4eOBZD2zjmSFSvf7Z1O8l3+ytWSuyjliGNcG0Pf1r5Qllprf6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c63d55d73bdc9232b1e12700e95c4dc77f1a720e5efd2b1d5b5669ba1648ef4","last_reissued_at":"2026-05-18T03:51:58.579177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:58.579177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Lie nilpotent varieties of associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Olga Finogenova","submitted_at":"2011-08-29T17:51:31Z","abstract_excerpt":"We consider associative algebras over a field. An algebra variety is said to be {\\em Lie nilpotent} if it satisfies a polynomial identity of the kind $[x_1, x_2, ..., x_n] = 0$ where $[x_1,x_2] = x_1x_2 - x_2x_1$ and $[x_1, x_2, ..., x_n]$ is defined inductively by $[x_1, x_2, ..., x_n]=[[x_1, x_2, ..., x_{n-1}],x_n]$. By Zorn's Lemma every non-Lie nilpotent variety contains a minimal such variety, called {\\em almost Lie nilpotent}, as a subvariety. A description of almost Lie nilpotent varieties for algebras over a field of characteristic 0 was made up by Yu.Mal'cev. 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