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.

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Information

Publisher

Academic Press

Year

2014

ISBN

9781483268064

Topic

Mathematics

Subtopic

Algebra

Index

Mathematics

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