Author: Samuel Aristide Nyobe Likeng
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
Locally Nilpotent Derivations on Polynomial Rings in Two Variables Over a Field of Characteristic Zero
Author: Samuel Aristide Nyobe Likeng
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
Locally Nilpotent Derivations and Their Rings of Constants
Author: Joseph Khoury
Publisher:
ISBN:
Category : Nilpotent Lie groups
Languages : en
Pages : 348
Book Description
Publisher:
ISBN:
Category : Nilpotent Lie groups
Languages : en
Pages : 348
Book Description
Locally Nilpotent Derivations of Polynomial Rings
Algebraic Theory of Locally Nilpotent Derivations
Author: Gene Freudenburg
Publisher: Springer
ISBN: 3662553503
Category : Mathematics
Languages : en
Pages : 333
Book Description
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.
Publisher: Springer
ISBN: 3662553503
Category : Mathematics
Languages : en
Pages : 333
Book Description
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
Author: Gene Freudenburg
Publisher: Springer Science & Business Media
ISBN: 3540295232
Category : Mathematics
Languages : en
Pages : 266
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3540295232
Category : Mathematics
Languages : en
Pages : 266
Book Description
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.
Affine Algebraic Geometry: Geometry Of Polynomial Rings
Author: Masayoshi Miyanishi
Publisher: World Scientific
ISBN: 981128010X
Category : Mathematics
Languages : en
Pages : 441
Book Description
Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by Iitaka and Kawamata.Readers will find the book covers vast basic material on an extremely rigorous level:
Publisher: World Scientific
ISBN: 981128010X
Category : Mathematics
Languages : en
Pages : 441
Book Description
Algebraic geometry is more advanced with the completeness condition for projective or complete varieties. Many geometric properties are well described by the finiteness or the vanishing of sheaf cohomologies on such varieties. For non-complete varieties like affine algebraic varieties, sheaf cohomology does not work well and research progress used to be slow, although affine spaces and polynomial rings are fundamental building blocks of algebraic geometry. Progress was rapid since the Abhyankar-Moh-Suzuki Theorem of embedded affine line was proved, and logarithmic geometry was introduced by Iitaka and Kawamata.Readers will find the book covers vast basic material on an extremely rigorous level:
Polynomial Automorphisms and the Jacobian Conjecture
Author: Arno van den Essen
Publisher: Springer Nature
ISBN: 3030605353
Category : Mathematics
Languages : en
Pages : 197
Book Description
This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000. Many new exciting results have been obtained in the past two decades, including the solution of Nagata's Conjecture, the complete solution of Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao spaces and counterexamples to the Cancellation problem in positive characteristic. These and many more results are discussed in detail in this work. The book is aimed at graduate students and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of each section.
Publisher: Springer Nature
ISBN: 3030605353
Category : Mathematics
Languages : en
Pages : 197
Book Description
This book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000. Many new exciting results have been obtained in the past two decades, including the solution of Nagata's Conjecture, the complete solution of Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao spaces and counterexamples to the Cancellation problem in positive characteristic. These and many more results are discussed in detail in this work. The book is aimed at graduate students and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of each section.
Integral Domains Inside Noetherian Power Series Rings: Constructions and Examples
Author: William Heinzer
Publisher: American Mathematical Soc.
ISBN: 1470466422
Category : Education
Languages : en
Pages : 426
Book Description
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Publisher: American Mathematical Soc.
ISBN: 1470466422
Category : Education
Languages : en
Pages : 426
Book Description
Power series provide a technique for constructing examples of commutative rings. In this book, the authors describe this technique and use it to analyse properties of commutative rings and their spectra. This book presents results obtained using this approach. The authors put these results in perspective; often the proofs of properties of classical examples are simplified. The book will serve as a helpful resource for researchers working in commutative algebra.
Polynomial Automorphisms
Author: Arno van den Essen
Publisher: Springer Science & Business Media
ISBN: 9783764363505
Category : Mathematics
Languages : en
Pages : 360
Book Description
Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.
Publisher: Springer Science & Business Media
ISBN: 9783764363505
Category : Mathematics
Languages : en
Pages : 360
Book Description
Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.
Integral Closure of Ideals, Rings, and Modules
Author: Craig Huneke
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446
Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Publisher: Cambridge University Press
ISBN: 0521688604
Category : Mathematics
Languages : en
Pages : 446
Book Description
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.