Noetherian algebras over algebraically closed fields

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dc.creatorBell, Jason P.
dc.date2006-06-09
dc.date.accessioned2026-07-07T07:17:07Z
dc.date.available2026-07-07T07:17:07Z
dc.descriptionLet $k$ 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/0606209
dc.identifierhttp://arxiv.org/abs/math/0606209
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113827
dc.subjectRings and Algebras
dc.titleNoetherian algebras over algebraically closed fields
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