{"paper":{"title":"The torsion subgroup of the additive group of a Lie nilpotent associative ring of class 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Galina Deryabina","submitted_at":"2013-08-19T20:55:29Z","abstract_excerpt":"Let $\\mathbb Z \\langle X \\rangle$ be the free unital associative ring freely generated by an infinite countable set $X = \\{ x_1,x_2, \\dots \\}$. Define a left-normed commutator $[x_1,x_2, \\dots, x_n]$ by $[a,b] = ab - ba$, $[a,b,c] = [[a,b],c]$. For $n \\ge 2$, let $T^{(n)}$ be the two-sided ideal in $\\mathbb Z \\langle X \\rangle$ generated by all commutators $[a_1,a_2, \\dots, a_n]$ $( a_i \\in \\mathbb Z \\langle X \\rangle )$. Let $T^{(3,2)}$ be the two-sided ideal of the ring $\\mathbb Z \\langle X \\rangle$ generated by all elements $[a_1, a_2, a_3, a_4]$ and $[a_1, a_2] [a_3, a_4, a_5]$ $(a_i \\in \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4172","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"}