Noetherian algebras over algebraically closed fields

Details Noetherian algebras over algebraically closed fields Noetherian algebras over algebraically closed fields

2006-06-09

arxiv.org/abs/math/0606209v1

Mathematics

Rings and Algebras

10 pages

Scientific paper

Let $k$ be an uncountable algebraically closed field and let $A$ be a countably generated left Noetherian $k$-algebra. Then we show that $A \otimes_k K$ is left Noetherian for any field extension $K$ of $k$. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over $k$ are finitely generated extensions of $k$. We give examples which show that $A\otimes_k K$ need not remain left Noetherian if the hypotheses are weakened.

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