Israel Journal of Mathematics

, Volume 73, Issue 3, pp 289–296 | Cite as

Gelfand-Kirillov dimension under base field extension

  • Quanshui Wu


LetFK 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 extensionFK and aK-algebraA such that GK dim F A=∞, but GK dim K A<∞.


Commutative Algebra Free Algebra Algebraic Extension Transcendental Extension Kirillov Dimension 
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Copyright information

© Hebrew University 1991

Authors and Affiliations

  • Quanshui Wu
    • 1
  1. 1.Institute of MathematicsFudan UniversityShanghaiPeople’s Republic of China

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