Affine Noetherian algebras and extensions of the base field II

Abstract

AbstractThe paper written many years ago by Resco and Small, constructed an example in prime characteristic of a finitely generated Noetherian ‐algebra that does not necessarily remain Noetherian under field extensions. After this work was completed, Yuri Medvedev, then at the University of Ottawa, visited Resco at the University of Oklahoma, read the paper, and suggested an approach using Jordan algebras that would yield a similar example in characteristic 0. This was announced in the paper by Resco and Small, but to our knowledge the details were never published nor even entirely verified. We take the opportunity to do this now, but stress that the key sequence and its relevant properties are due to Medvedev. Also, Resco suggested avoiding Jordan algebras and working directly and ring theoretically with the exterior algebra. This is the approach we take.