{"paper":{"title":"Relations in universal Lie nilpotent associative algebras of class 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Eudes Antonio da Costa","submitted_at":"2013-06-18T18:44:38Z","abstract_excerpt":"Let $K$ be a unital associative and commutative ring and let $K \\langle X \\rangle$ be the free unital associative $K$-algebra on a non-empty set $X$ of free generators. Define a left-normed commutator $[a_1, a_2, \\dots , a_n]$ inductively by $[a_1, a_2] = a_1 a_2 - a_2 a_1$, $[a_1, \\dots , a_{n-1}, a_n] = [[a_1, \\dots , a_{n-1}], a_n]$ $(n \\ge 3)$. For $n \\ge 2$, let $T^{(n)}$ be the two-sided ideal in $K \\langle X \\rangle$ generated by all commutators $[a_1,a_2, \\dots , a_n]$ $( a_i \\in K \\langle X \\rangle )$.\n  It can be easily seen that the ideal $T^{(2)}$ is generated (as a two-sided ideal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4294","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"}