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Collected Works: Selected Works of Ellis Kolchin with Commentary by Phyllis J. Cassidy, Alexandru Buium and E. R. Kolchin (1999, Hardcover)
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-100821805428
ISBN-139780821805428
eBay Product ID (ePID)687731
Product Key Features
Number of Pages640 Pages
Publication NameSelected Works of Ellis Kolchin with Commentary
LanguageEnglish
SubjectAlgebra / General
Publication Year1999
TypeTextbook
Subject AreaMathematics
AuthorPhyllis J. Cassidy, Alexandru Buium, E. R. Kolchin
SeriesCollected Works
FormatHardcover
Dimensions
Item Height0.6 in
Item Weight23.5 Oz
Item Length9.8 in
Item Width5.9 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN98-049445
Dewey Edition21
Series Volume Number12
IllustratedYes
Dewey Decimal512/.56
Table Of ContentPicard-Vessiot theory of partial differential fields The notion of dimension in the theory of algebraic differential equations Part I. The Papers of Ellis Kolchin: On certain ideals of differential polynomials On the basis theorem for infinite systems of differential polynomials On the exponents of differential ideals On the basis theorem for differential systems Extensions of differential fields. I Extensions of differential fields. II Algebraic matric groups The Picard-Vessiot theory of homogeneous linear ordinary differential equations Extensions of differential fields. III Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations On certain concepts in the theory of algebraic matric groups Existence theorems connected with the Picard-Vessiot theory of homogeneous linear ordinary differential equations Algebraic groups and differential equations Two proofs of a theorem on algebraic groups Picard-Vessiot theory of partial differential fields Galois theory of differential fields Differential fields and group varieties (First lecture) Differential fields and group varieties (Second lecture) On the Galois theory of differential fields Algebraic groups and the Galois theory of differential fields Rational approximation to the solutions of algebraic differential equations Existence of invariant bases Abelian extensions of differential fields Le theoreme de la base finie pour les polynomes differentiels The notion of dimension in the theory of algebraic differential equations Singular solutions of algebraic differential equations and a lemma of Arnold Shapiro Some problems in differential algebra Algebraic groups and algebraic dependence Differential polynomials and strongly normal extensions Constrained extensions of differential fields Differential equations in a projective space and linear dependence over a projective variety Differential algebraic groups Differential algebraic structures On universal extensions of differential fields Differential algebraic groups A problem on differential polynomials Painleve transcendent Part II. Commentary: Algebraic groups and Galois theory in the work of Ellis R. Kolchin by A. Borel Direct and inverse problems in differential Galois theory by M. F. Singer Les corps differentiellement clos, compagnons de route de la theorie des modeles by B. Poizat Differential algebraic geometry and differential algebraic groups: From algebraic differential equation to Diophantine geometry by A. Buium and P. J. Cassidy.
SynopsisThe work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This volume assembles Kolchin's mathematical papers, contributing solidly to the archive on construction of modern differential algebra. This collection of Kolchin's comprehensive papers is an aid to the student of differential algebra. In 1910, Ritt created a theory of algebraic differential equations modelled not on the existing transcendental methods of Lie, but rather on the new algebra being developed by E. Noether and B. van der Waerden. Building on Ritt's foundation, and deeply influenced by Weil and Chevalley, Kolchin opened up Ritt theory to modern algebraic geometry. In so doing, he led differential geometry in a new direction. By creating differential algebraic geometry and the theory of differential algebraic groups, Kolchin provided the foundation for a new geometry that has led to both a striking and an original approach to arithmetic algebraic geomet., The work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This volume assembles Kolchin's mathematical papers, contributing solidly to the archive on construction of modern differential algebra. This collection of Kolchin's clear and comprehensive papers - in themselves constituting a history of the subject - is an invaluable aid to the student of differential algebra. In 1910, Ritt created a theory of algebraic differential equations modeled not on the existing transcendental methods of Lie, but rather on the new algebra being developed by E. Noether and B. van der Waerden.Building on Ritt's foundation, and deeply influenced by Weil and Chevalley, Kolchin opened up Ritt theory to modern algebraic geometry. In so doing, he led differential geometry in a new direction. By creating differential algebraic geometry and the theory of differential algebraic groups, Kolchin provided the foundation for a 'new geometry' that has led to both a striking and an original approach to arithmetic algebraic geometry. Intriguing possibilities were introduced for a new language for nonlinear differential equations theory. The volume includes commentary by A. Borel, M. Singer, and B. Poizat.Also Buium and Cassidy trace the development of Kolchin's ideas, from his important early work on the differential Galois theory to his later groundbreaking results on the theory of differential algebraic geometry and differential algebraic groups. Commentaries are self-contained with numerous examples of various aspects of differential algebra and its applications. Central topics of Kolchin's work are discussed, presenting the history of differential algebra and exploring how his work grew from and transformed the work of Ritt. New directions of differential algebra are illustrated, outlining important current advances. Prerequisite to understanding the text is a background at the beginning graduate level in algebra, specifically commutative algebra, the theory of field extensions, and Galois theory., The work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This volume assembles Kolchin's mathematical papers, contributing solidly to the archive on construction of modern differential algebra. This collection of Kolchin's clear and comprehensive papers--in themselves constituting a history of the subject--is an invaluable aid to the student of differential algebra. In 1910, Ritt created a theory of algebraic differential equations modeled not on the existing transcendental methods of Lie, but rather on the new algebra being developed by E. Noether and B. van der Waerden. Building on Ritt's foundation, and deeply influenced by Weil and Chevalley, Kolchin opened up Ritt theory to modern algebraic geometry. In so doing, he led differential geometry in a new direction. By creating differential algebraic geometry and the theory of differential algebraic groups, Kolchin provided the foundation for a "new geometry" that has led to both a striking and an original approach to arithmetic algebraic geometry. Intriguing possibilities were introduced for a new language for nonlinear differential equations theory. The volume includes commentary by A. Borel, M. Singer, and B. Poizat. Also Buium and Cassidy trace the development of Kolchin's ideas, from his important early work on the differential Galois theory to his later groundbreaking results on the theory of differential algebraic geometry and differential algebraic groups. Commentaries are self-contained with numerous examples of various aspects of differential algebra and its applications. Central topics of Kolchin's work are discussed, presenting the history of differential algebra and exploring how his work grew from and transformed the work of Ritt. New directions of differential algebra are illustrated, outlining important current advances. Prerequisite to understanding the text is a background at the beginning graduate level in algebra, specifically commutative algebra, the theory of field extensions, and Galois theory., The work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This book assembles Kolchin's mathematical papers.
LC Classification NumberQA247.4.K65 1999
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