{"paper":{"title":"Products of several commutators in a Lie nilpotent associative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Galina Deryabina","submitted_at":"2016-10-11T00:14:15Z","abstract_excerpt":"Let $F$ be a field of characteristic $\\ne 2,3$ and let $A$ be a unital associative $F$-algebra. Define a left-normed commutator $[a_1, a_2, \\dots , a_n]$ $(a_i \\in A)$ recursively 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 $T^{(n)} (A)$ be the two-sided ideal in $A$ generated by all commutators $[a_1, a_2, \\dots , a_n]$ ($a_i \\in A )$. Define $T^{(1)} (A) = A$.\n  Let $k, \\ell$ be integers such that $k > 0$, $0 \\le \\ell \\le k$. Let $m_1, \\dots , m_k$ be positive integers such that $\\ell$ of them are odd and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03136","kind":"arxiv","version":3},"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"}