- 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
Buy this book
- 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)
- Table of contents (12 chapters)
-
-
Introduction
Pages 1-7
-
First Principles
Pages 9-33
-
Further Properties of Locally Nilpotent Derivations
Pages 35-47
-
Polynomial Rings
Pages 49-82
-
Dimension Two
Pages 83-106
-
Table of contents (12 chapters)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Algebraic Theory of Locally Nilpotent Derivations
- Authors
-
- Gene Freudenburg
- 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
