2014/05/29 by Gene Freudenburg
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Affine transformation #Affine variety #Commutative Algebra and Its Applications #Embedding #Field (mathematics) #Locally nilpotent #Nilpotent #Polynomial and algebraic computation #Polynomial ring #Ring (chemistry) #math.AC #msc:13B25 #msc:14R20
paper · pdf · doi:10.1215/21562261-3089136
published as Kyoto J. Math. 55, no. 3 (2015), 663-672 · 7 pages
arxiv created 2014/05/29 · openalex publication_date 2015/09/01 · arxiv updated 2015/11/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let R be an affine k-domain over the field k. The paper’s main result is that if R admits a nontrivial embedding in a polynomial ring K[s] for some field K containing k, then R can be embedded in a polynomial ring F[t] which extends R algebraically. This theorem can be applied to subrings of a ring which admits a nonzero locally nilpotent derivation. In this way, we obtain a concise new proof of the cancellation theorem for rings of transcendence degree one for fields of characteristic 0.