Contributions to Algebra

A Collection of Papers Dedicated to Ellis Kolchin

Hyman Bass, Phyllis J. Cassidy, Jerald Kovacic

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780120805501
• eBook ISBN:
  9781483268064
• Topic: Mathématiques
• Subtopic: Algèbre

Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin provides information pertinent to commutative algebra, linear algebraic group theory, and differential algebra. This book covers a variety of topics, including complex analysis, logic, K-theory, stochastic matrices, and differential geometry. Organized into 29 chapters, this book begins with an overview of the influence that Ellis Kolchin's work on the Galois theory of differential fields has had on the development of differential equations. This text then discusses the background model theoretic work in differential algebra and discusses the notion of model completions. Other chapters consider some properties of differential closures and some immediate consequences and include extensive notes with proofs. This book discusses as well the problems in finite group theory in finding the complex finite projective groups of a given degree. The final chapter deals with the finite forms of quasi-simple algebraic groups. This book is a valuable resource for students.

Table of contents

• Front Cover
• Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin
• Copyright Page
• Table of Contents
• Dedication
• List of contributors
• Preface
• Chapter 1. Quadratic modules over polynomial rings
• Chapter 2. The action of the universal modular group on certain boundary points
• Chapter 3. Differentially closed fields: a model-theoretic tour
• Chapter 4. On finite projective groups
• Chapter 5. Unipotent differential algebraic groups
• Chapter 6. Solutions in the general solution
• Chapter 7. Folk theorems on elliptic equations
• Chapter 8. Limit properties of stochastic matrices
• Chapter 9. A fixed-point characterization of linearly reductive groups
• Chapter 10. Orthogonal and unitary invariants of families of subspaces
• Chapter 11. The Macdonald–Kac formulas as a consequence of the Euler–Poincaré principle
• Chapter 12. The characters of reductive p-adic groups
• Chapter 13. Basic constructions in group extension theory
• Chapter 14. On the hyperalgebra of a semisimple algebraic group
• Chapter 15. A notion of regularity for differential local algebras
• Chapter 16. The Engel–Kolchin theorem revisited
• Chapter 17. Prime differential ideals in differential rings
• Chapter 18. Constrained cohomology
• Chapter 19. The integrability condition of deformations of CR structures
• Chapter 20. Noetherian rings with many derivations
• Chapter 21. Hopf maps and quadratic forms over Z
• Chapter 22. Families of subgroup schemes of formal groups
• Chapter 23. An effective lower bound on the "diophantine" approximation of algebraic functions by rational functions (II)
• Chapter 24. On elementary, generalized elementary, and liouvillian extension fields
• Chapter 25. Derivations and valuation rings
• Chapter 26. On theorems of Lie–Kolchin, Borel, and Lang
• Chapter 27. A differential-algebraic study of the intrusion of logarithms into asymptotic expansions
• Chapter 28. A "theorem of Lie–Kolchin" for trees
• Chapter 29. Regular elements in anisotropic tori