Abstract
LetF ⊂K be a field extension,A be aK-algebra. It is proved that, in general, GK dim F A≥GK dim K A+tr F (K). For commutative algebras or Noetherian P.I. algebras, the equality holds. Two examples are also constructed to show that: (i) there exists an algebraA such that GK dim F A=GK dim K A+tr F (K)+1; (ii) there exists an algebraic extensionF ⊂K and aK-algebraA such that GK dim F A=∞, but GK dim K A<∞.
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Wu, Q. Gelfand-Kirillov dimension under base field extension. Israel J. Math. 73, 289–296 (1991). https://doi.org/10.1007/BF02773842
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DOI: https://doi.org/10.1007/BF02773842