{"paper":{"title":"$\\sigma$-Biderivations and $\\sigma$-commuting maps of triangular algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"C\\'andido Mart\\'in Gonz\\'alez, Joe Repka, Juana S\\'anchez-Ortega","submitted_at":"2013-12-13T23:11:19Z","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 bilinear map $D: \\A \\times \\A \\to \\A$ is said to be a $\\sigma$-biderivation of $\\A$ if it is a $\\sigma$-derivation in each component. An additive map $\\Theta$ of $\\A$ is $\\sigma$-commuting if it satisfies $\\Theta(x)x - \\sigma(x)\\Theta(x) = 0$, for all $x \\in \\A$. In this paper, we introduce the notions of inner and extremal $\\sigma$-biderivations and of proper $\\sigma$-commuting maps. One of our main results s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3980","kind":"arxiv","version":2},"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"}