{"paper":{"title":"Unital locally matrix algebras and Steinitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Bogdana Oliynyk, Oksana Bezushchak","submitted_at":"2019-07-26T12:13:50Z","abstract_excerpt":"An $F$-algebra $A$ with unit $1$ is said to be a locally matrix algebra if an arbitrary finite collection of elements $a_1,$ $\\ldots,$ $a_s $ from $ A$ lies in a subalgebra $B$ with $1$ of the algebra $A$, that is isomorphic to a matrix algebra $M_n(F),$ $n\\geq 1.$ To an arbitrary unital locally matrix algebra $A$ we assign a Steinitz number $\\mathbf{n}(A)$ and study a relationship between $\\mathbf{n}(A)$ and $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11506","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"}