{"paper":{"title":"Automatic additivity for injective Jordan semi-triple maps on structural matrix rings over division rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ilja Gogi\\'c, Mateo Toma\\v{s}evi\\'c","submitted_at":"2026-06-02T10:32:31Z","abstract_excerpt":"Let $\\mathbb D$ be a division ring, and let $\\mathcal{R}\\subseteq M_n(\\mathbb{D})$ be a structural matrix ring over $\\mathbb{D}$, that is, the subring of $M_n(\\mathbb{D})$ supported on the ordered pairs of a preorder on $\\{1,\\ldots,n\\}$. We study injective Jordan semi-triple maps $\\phi:\\mathcal{R}\\to M_n(\\mathbb{D})$, namely injective maps satisfying \\[\n  \\phi(XYX)=\\phi(X)\\phi(Y)\\phi(X), \\qquad \\text{for all } X,Y\\in\\mathcal{R}. \\] Assuming that the centre of $\\mathbb{D}$ has more than two elements, we give a criterion for automatic additivity and show that there are exactly two obstructions. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03454","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.03454/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}