{"paper":{"title":"Non-finitely based varieties of right alternative metabelian algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexey Kuz'min","submitted_at":"2015-02-18T22:13:54Z","abstract_excerpt":"Since 1976, it is known from the paper by V. P. Belkin that the variety $\\mathrm{RA_2}$ of right alternative metabelian (solvable of index 2) algebras over an arbitrary field is not Spechtian (contains non-finitely based subvarieties). In 2005, S. V. Pchelintsev proved that the variety generated by the Grassmann $\\mathrm{RA_2}$-algebra of finite rank $r$ over a field $\\mathcal{F}$, for $\\mathrm{char}(\\mathcal{F})\\neq2$, is Spechtian iff $r=1$. We construct a non-finitely based variety $\\mathfrak{M}$ generated by the Grassmann $\\mathcal{V}$-algebra of rank $2$ of certain finitely based subvarie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05431","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"}