{"paper":{"title":"$\\sigma$-Mappings of triangular algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Juana S\\'anchez-Ortega","submitted_at":"2013-12-17T04:30:05Z","abstract_excerpt":"Let $A$ be an algebra and $\\sigma$ an automorphism of $A$. A linear map $d$ of $A$ is called a $\\sigma$-derivation of $A$ if $d(xy) = d(x)y + \\sigma(x)d(y)$, for all $x, y \\in A$. A linear map $D$ is said to be a generalized $\\sigma$-derivation of $A$ if there exists a $\\sigma$-derivation $d$ of $A$ such that $D(xy) = D(x)y + \\sigma(x)d(y)$, for all $x, y \\in A$. An additive map $\\Theta$ of $A$ is $\\sigma$-centralizing if $\\Theta(x)x - \\sigma(x)\\Theta(x) \\in Z(A)$, for all $x \\in A$. In this paper, precise descriptions of generalized $\\sigma$-derivations and $\\sigma$-centralizing maps of trian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4635","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"}