2006/06/09 by Jason P. Bell, Bell, Jason P.
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.48550/arxiv.math/0606209
10 pages
arxiv created 2006/06/09 · openalex publication_date 2006/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A ⊗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⊗k K need not remain left Noetherian if the hypotheses are weakened.