{"paper":{"title":"Derivations and 2-local derivations on matrix algebras over commutative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"Jiankui Li, Wenbo Huang, Wenhua Qian","submitted_at":"2016-11-03T03:52:48Z","abstract_excerpt":"We characterize derivations and 2-local derivations from $M_{n}(\\mathcal{A})$ into $M_{n}(\\mathcal{M})$, $n \\ge 2$, where $\\mathcal{A}$ is a unital algebra over $\\mathbb{C}$ and $\\mathcal{M}$ is a unital $\\mathcal{A}$-bimodule. We show that every derivation $D: M_{n}(\\mathcal{A}) \\to M_{n}(\\mathcal{M})$, $n \\ge 2,$ is the sum of an inner derivation and a derivation induced by a derivation from $\\mathcal{A}$ to $\\mathcal{M}$. We say that $\\mathcal{A}$ commutes with $\\mathcal{M}$ if $am=ma$ for every $a\\in\\mathcal{A}$ and $m\\in\\mathcal{M}$. If $\\mathcal{A}$ commutes with $\\mathcal{M}$ we prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00871","kind":"arxiv","version":3},"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"}