{"paper":{"title":"On Lie nilpotent associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Claud W. G. Dias Jr","submitted_at":"2017-09-17T23:47:11Z","abstract_excerpt":"Let $G$ be a group generated by a set $X$. It is well known and easy to check that \\[ [g_1, g_2, \\dots ,g_n] = 1 \\mbox{ for all } g_i \\in G \\qquad \\iff \\qquad [x_1, x_2, \\dots , x_n] =1 \\mbox{ for all } x_i \\in X. \\] Let $L$ be a Lie algebra generated by a set $X$. Then it is also well known and easy to check that \\[ [h_1, h_2, \\dots , h_n] = 0 \\mbox{ for all } h_i \\in L \\qquad \\iff \\qquad [x_1, x_2, \\dots ,x_n] = 0 \\mbox{ for all } x_i \\in X. \\]\n  Now let $A$ be a unital associative algebra generated by a set $X$. Then the assertion similar to the above does not hold: for $n > 2$, it is easy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05728","kind":"arxiv","version":1},"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"}