{"paper":{"title":"Introduction into Calculus over Division Ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Aleks Kleyn","submitted_at":"2008-12-30T05:55:44Z","abstract_excerpt":"Based on twin representations of division ring in an Abelian group I consider $D$\\Hyph vector spaces over division ring. Morphism of $D$\\Hyph vector spaces is linear map of $D$\\Hyph vector spaces.\n  I consider derivative of function $f$ of continuous division ring as linear map the most close to function $f$. I explore expansion of map into Taylor series and method to find solution of differential equation.\n  The norm in $D$\\Hyph vector space allows considering of continuous mapping of $D$\\Hyph vector spaces. Differential of mapping $f$ of $D$\\Hyph vector spaces is defined as linear mapping th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4763","kind":"arxiv","version":7},"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"}