{"paper":{"title":"Estimations of the particular periodicity in case of the extremal periods in Shirshov's Height theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Mikhail Kharitonov","submitted_at":"2011-08-31T17:35:22Z","abstract_excerpt":"Let us recall the well-known Shirshov's Height Theorem. \"Let A be a finitely generated algebra of degree d. Then there exists a finite set Y which is the subset of A that A has and an integer h' = h(A) such that A has Shirshov's height h' over set Y. For Y we may take the set of words of length <d. Such Y is called a Shirshov's base of algebra A.\" Shirshov's original proof was purely combinatorical, but did not provide a reasonable upper estimate for the height. Kolotov obtained an estimate for h(A) < s^(s^m) (m = deg(A), and s is the number of generators) in 1981. I. Zelmanov asked for an exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6295","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"}