{
  "annotation_id": "f14dab4c-3f8c-4657-88e6-41c7daadecf2",
  "date_created": "2026-02-17T05:53:08.516000Z",
  "date_modified": "2026-02-17T05:53:08.516000Z",
  "file_hash": "9d33da0cca82586ca46fb416ff5dfb499f7a198c35ef7c6493a8e9a5c4d2c34d",
  "private": false,
  "record": {
    "abstract": "Let $A$ be a unital locally matrix algebra. Among the examples of such algebras are: (1) an infinite tensor product $\\otimes M_{n_i}(\\mathbb{F})$ of matrix algebras over a field $\\mathbb{F}$, and (2) the Clifford algebra of a nondegenerate quadratic form on an infinite-dimensional vector space over an algebraically closed field of characteristic different from $2$.\n  We describe linear mappings $A \\to B$ between unital locally matrix algebras that preserve the normalized rank. When $\\mathbb{F}$ is a field of real or complex numbers, we also describe linear mappings $A \\to A$ that preserve the normalized determinant.",
    "arxiv_id": "2601.06950",
    "authors": [
      "Oksana Bezushchak"
    ],
    "categories": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Normalized Rank- and Determinant-Preserving Mappings of Locally Matrix Algebras",
    "url": "https://arxiv.org/abs/2601.06950",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "75b515e9-78cf-40cc-97c7-a31326eee8a0",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}