{"paper":{"title":"The subalgebra of graded central polynomials of an associative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Krasilnikov, Galina Deryabina","submitted_at":"2014-09-28T18:00:57Z","abstract_excerpt":"Let $F$ be a field and let $F \\langle X \\rangle$ be the free unital associative $F$-algebra on the free generating set $X = \\{ x_1, x_2, \\dots \\}$. A subalgebra (a vector subspace) $V$ in $F \\langle X \\rangle$ is called a $T$-subalgebra (a $T$-subspace) if $\\phi (V) \\subseteq V$ for all endomorphisms $\\phi$ of $F \\langle X \\rangle$. For an algebra $G$, its central polynomials form a $T$-subalgebra $C(G)$ in $F \\langle X \\rangle$. Over a field of characteristic $p > 2$ there are algebras $G$ whose algebras of all central polynomials $C (G)$ are not finitely generated as $T$-subspaces in $F \\lan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7937","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"}