Non-Finitely Generated Kernels

  • Gene Freudenburg
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 136)


This chapter shows that the solution to the Finiteness Problem for non-linear algebraic G a -actions is, in general, negative. In particular, we will explore the famous examples of Paul Roberts and some of the rich theory which has flowed from them. These were the first examples to (in effect) show that the kernel of a locally nilpotent derivation on a polynomial ring is not always finitely generated.


Prime Ideal Polynomial Ring Hilbert Series Coordinate Ring Finiteness Theorem 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Gene Freudenburg
    • 1
  1. 1.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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