{"paper":{"title":"Lectures on Linear Algebra 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":"2007-01-09T02:43:20Z","abstract_excerpt":"In this book i treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a new picture.\n  Matrices allow two products linked by transpose. Biring is algebra which defines on the set two correlated structures of the ring.\n  As in the commutative case, solutions of a system of linear equations build up right or left vector space depending on type of system. We study vector spaces together with the system of linear equations because the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701238","kind":"arxiv","version":6},"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"}