{"paper":{"title":"Simultaneous Embeddings of Finite Dimensional Division Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"David J Saltman, Louis Rowen","submitted_at":"2010-09-07T08:30:14Z","abstract_excerpt":"A celebrated theorem of P.M.Cohn says that for any two division rings (not necessarily finite dimensional) over a field F, their amalgamated product over F is a domain which can be embedded in a division ring. Note that even with the two initial division rings begin finite dimensional over their centers, the resulting division ring is never finite dimensional over its center. Perhaps this led Lance Small to ask the following question. Assume $F_1$ and $F_2$ are fields with the same characteristic. Small asked whether any two division algebras $D_1/F_1$ and $D_2/F_2$ can be embedded in some thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1226","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"}