Contributions to Algebra : A Collection of Papers Dedicated to Ellis Kolchin

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv Inside Front Cover, Page v List of contributors, Pages xv-xvi Preface, Pages xvii-xxii Quadratic modules over polynomial rings, Pages 1-23, Hyman Bass The action of the universal modular group on certain boundary points, Pages 25-36, Lipman Bers Differentially closed fields: a model-theoretic tour, Pages 37-61, Lenore Blum On finite projective groups, Pages 63-82, Richard Brauer Unipotent differential algebraic groups, Pages 83-115, Phyllis J. Cassidy Solutions in the general solution, Pages 117-128, Richard M. Cohn Folk theorems on elliptic equations, Pages 129-134, Jean Dieudonné Limit properties of stochastic matrices, Pages 135-149, Samuel Eilenberg, Alex Heller A fixed-point characterization of linearly reductive groups, Pages 151-155, J. Fogarty, P. Norman Orthogonal and unitary invariants of families of subspaces, Pages 157-164, P.X. Gallagher, R.J. Proulx The Macdonald-Kac formulas as a consequence of the Euler-Poincaré principle, Pages 165-173, Howard Garland, James Lepowsky The characters of reductive p-adic groups, Pages 175-182, Harish-Chandra Basic constructions in group extension theory, Pages 183-201, G. Hochschild On the hyperalgebra of a semisimple algebraic group, Pages 203-210, J.E. Humphreys A notion of regularity for differential local algebras, Pages 211-232, Joseph Johnson The Engel–Kolchin theorem revisited, Pages 233-237, Irving Kaplansky Prime differential ideals in differential rings, Pages 239-249, William F. Keigher Constrained cohomology, Pages 251-266, J. Kovacic The integrability condition of deformations of CR structures, Pages 267-278, Masatake Kuranishi Noetherian rings with many derivations, Pages 279-294, Hideyuki Matsumura Hopf maps and quadratic forms over Z, Pages 295-304, Takashi Ono Families of subgroup schemes of formal groups, Pages 305-319, Frans Oort An effective lower bound on the “diophantine” approximation of algebraic functions by rational functions (II), Pages 321-327, Charles F. Osgood On elementary, generalized elementary, and liouvillian extension fields, Pages 329-342, Maxwell Rosenlicht, Michael Singer Derivations and valuation rings, Pages 343-347, A. Seidenberg On theorems of Lie-Kolchin, Borel, and Lang, Pages 349-354, Robert Steinberg A differential-algebraic study of the intrusion of logarithms into asymptotic expansions, Pages 355-375, Walter Strodt A “theorem of Lie-Kolchin” for trees, Pages 377-388, J. Tits Regular elements in anisotropic tori, Pages 389-424, F.D. Veldkamp