{"paper":{"title":"Estimates related to Shirshov height theorem (PhD Thesis)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Mikhail Kharitonov","submitted_at":"2015-11-15T16:05:47Z","abstract_excerpt":"In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: $\"$Suppose that $F_{2,m}$ is a $2$-generated associative ring with the identity $x^m=0$. Is it true, that the nilpotency degree of $F_{2,m}$ has exponential growth?$\"$ We show that the nilpotency degree of $l$-generated associative algebra with the identity $x^d=0$ is smaller than $\\Psi(d,d,l)$, where $\\Phi(n,d,l)=l(nd)^{C\\log(nd)}$ and $C$ is a constant. We give the definitive answer to E. I. Zelmanov by this result. It is the consequence of one fact, which is based on combinatorics of words. Let $l$, $n$ and $d\\ge n$ b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04721","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"}