{"paper":{"title":"Automorphisms of the endomorphism semigroup of a free commutative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"A. Belov-Kanel, R. Lipyanski","submitted_at":"2009-03-27T16:16:02Z","abstract_excerpt":"We describe the automorphism group of the endomorphism semigroup $\\End(K[x_1,...,x_n])$ of ring $K[x_1,...,x_n]$ of polynomials over an {\\it arbitrary} field $K$. A similar result is obtained for automorphism group of the category of finitely generated free commutative-associative algebras of the variety $\\mathcal{CA}$ commutative algebras. This solves two problems posed by B. Plotkin (\\cite{24}, Problems 12 and 15).\n  More precisely, we prove that if $\\varphi\\in \\Aut\\End(K[x_1,...,x_n])$ then there exists a semi-linear automorphism $s:K[x_1,...,x_n]\\to K[x_1,...,x_n]$ such that $\\varphi(g)=s\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4839","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"}