Overview

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.

Full Product Details

Author:   Gene Freudenburg
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2006
Volume:   136
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642067327

ISBN 10:   3642067328
Pages:   261
Publication Date:   16 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

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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)

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)

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)

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