Locally Nilpotent Derivations and Their Rings of Constants
Title | Locally Nilpotent Derivations and Their Rings of Constants PDF eBook |
Author | Joseph Khoury |
Publisher | |
Pages | 348 |
Release | 2001 |
Genre | Nilpotent Lie groups |
ISBN |
Algebraic Theory of Locally Nilpotent Derivations
Title | Algebraic Theory of Locally Nilpotent Derivations PDF eBook |
Author | Gene Freudenburg |
Publisher | Springer |
Pages | 333 |
Release | 2017-09-08 |
Genre | Mathematics |
ISBN | 3662553503 |
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
Algebraic Theory of Locally Nilpotent Derivations
Title | Algebraic Theory of Locally Nilpotent Derivations PDF eBook |
Author | Gene Freudenburg |
Publisher | Springer Science & Business Media |
Pages | 266 |
Release | 2007-07-18 |
Genre | Mathematics |
ISBN | 3540295232 |
This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen 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. The book also includes a wealth of pexamples and open problems.
Locally Finite and Locally Nilpotent Derivations with Applications to Polynomial Flows, Morphisms and Ga-actions
Title | Locally Finite and Locally Nilpotent Derivations with Applications to Polynomial Flows, Morphisms and Ga-actions PDF eBook |
Author | Arno van den Essen |
Publisher | |
Pages | |
Release | 1992 |
Genre | |
ISBN |
Locally finite and locally nilpotent derivations with applications to polynomial flows and polynomial morphisms
Title | Locally finite and locally nilpotent derivations with applications to polynomial flows and polynomial morphisms PDF eBook |
Author | Arno van den Essen |
Publisher | |
Pages | 12 |
Release | 1990 |
Genre | |
ISBN |
Affine Algebraic Geometry
Title | Affine Algebraic Geometry PDF eBook |
Author | Jaime Gutierrez |
Publisher | American Mathematical Soc. |
Pages | 288 |
Release | 2005 |
Genre | Mathematics |
ISBN | 0821834762 |
A Special Session on affine and algebraic geometry took place at the first joint meeting between the American Mathematical Society (AMS) and the Real Sociedad Matematica Espanola (RSME) held in Seville (Spain). This volume contains articles by participating speakers at the Session. The book contains research and survey papers discussing recent progress on the Jacobian Conjecture and affine algebraic geometry and includes a large collection of open problems. It is suitable for graduate students and research mathematicians interested in algebraic geometry.
Integral Closure of Ideals, Rings, and Modules
Title | Integral Closure of Ideals, Rings, and Modules PDF eBook |
Author | Craig Huneke |
Publisher | Cambridge University Press |
Pages | 446 |
Release | 2006-10-12 |
Genre | Mathematics |
ISBN | 0521688604 |
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.