Let be an affine -domain over the field . The paper’s main result is that if admits a nontrivial embedding in a polynomial ring for some field containing , then can be embedded in a polynomial ring which extends 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 .
"An affine version of a theorem of Nagata." Kyoto J. Math. 55 (3) 663 - 672, September 2015. https://doi.org/10.1215/21562261-3089136