Encyclopaedia of Mathematical Sciences

Algebraic Theory of Locally Nilpotent Derivations

Authors: Freudenburg, Gene

  • First monograph on topic
  • Explores the theory and application of locally nilpotent derivations
  • Provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based
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  • ISBN 978-3-540-29523-5
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Softcover $159.00
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About this book

This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. 
The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings. Topics of special interest include: progress in the dimension three case, finiteness questions (Hilbert’s 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. The reader will also find a wealth of pertinent examples and open problems and an up-to-date resource for research.  

Reviews

From the reviews:

"In the volume under review, the author gives a detailed description of the subject covering all the important results … . the book has a wealth of examples and the Epilogue details some important open problems in the area. … is accessible to less advanced graduate students. It is a valuable addition to the literature and am sure would be very helpful to the interested student and researcher alike." (N. Mohan Kumar, Zentralblatt MATH, Vol. 1121 (23), 2007)


Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-540-29523-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $159.00
price for USA
  • ISBN 978-3-642-06732-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Theory of Locally Nilpotent Derivations
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
136
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-29523-5
DOI
10.1007/978-3-540-29523-5
Softcover ISBN
978-3-642-06732-7
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XI, 261
Topics