{"paper":{"title":"Free algebras and free groups in Ore extensions and free group algebras in division rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jairo Z. Goncalves, Jason P. Bell","submitted_at":"2015-07-31T09:45:33Z","abstract_excerpt":"Let $K$ be a field of characteristic zero, let $\\sigma$ be an automorphism of $K$ and let $\\delta$ be a $\\sigma$-derivation of $K$. We show that the division ring $D=K(x;\\sigma,\\delta)$ either has the property that every finitely generated subring satisfies a polynomial identity or $D$ contains a free algebra on two generators over its center. In the case when $K$ is finitely generated over $k$ we then see that for $\\sigma$ a $k$-algebra automorphism of $K$ and $\\delta$ a $k$-linear derivation of $K$, $K(x;\\sigma)$ having a free subalgebra on two generators is equivalent to $\\sigma$ having inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08811","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"}