A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Author(s): Karlheinz Spindler
Edition: 1
Publisher: M. DEKKER, CRC PRESS
Year: 1994
Language: English
Pages: 569
City: New York
Tags: Rings, Fields
TABLE OF CONTENTS
CHAPTER 1...........................INTRODUCTION: THE ART OF DOING ARITHMETIC
CHAPTER 2.......................... RINGS AND RING HOMOMORPHISMS
CHAPTER 3...........................INTEGRAL DOMAINS AND FIELDS
CHAPTER 4...........................POLYNOMIAL AND POWER SERIES RINGS
CHAPTER 5...........................IDEALS AND QUOTIENT RINGS
CHAPTER 6...........................IDEALS IN COMMUTATIVE RINGS
CHAPTER 7...........................FACTORIZATION IN INTEGRAL DOMAINS
CHAPTER 8...........................FACTORIZATION IN POLYNOMIAL AND POWER SERIES RINGS
CHAPTER 9...........................NUMBER-THEORETICAL APPLICATIONS OF UNIQUE FACTORIZATION
CHAPTER 10..........................MODULES AND INTEGRAL RING EXTENSIONS
CHAPTER 11..........................NOETHERIAN RINGS
CHAPTER 12..........................FIELD EXTENSIONS
CHAPTER 13..........................SPLITTING FIELDS AND NORMAL EXTENSIONS
CHAPTER 14..........................SEPARABILITY OF FIELD EXTENSIONS
CHAPTER 15..........................FIELD THEORY AND INTEGRAL RING EXTENSIONS
CHAPTER 16..........................AFFINE ALGEBRAS
CHAPTER 17..........................RING THEORY AND ALGEBRAIC GEOMETRY
CHAPTER 18..........................LOCALIZATION
CHAPTER 19..........................FACTORIZATION OF IDEALS
CHAPTER 20..........................INTRODUCTION TO GALOIS THEORY: SOLVING POLYNOMIAL EQUATIONS
CHAPTER 21..........................THE GALOIS GROUP OF A FIELD EXTENSION
CHAPTER 22..........................ALGEBRAIC GALOIS EXTENSIONS
CHAPTER 23..........................THE GALOIS GROUP OF A POLYNOMIAL
CHAPTER 24..........................ROOTS OF UNITY AND CYCLOTOMIC POLYNOMIALS
CHAPTER 25..........................PURE EQUATIONS AND CYCLIC EXTENSIONS
CHAPTER 26..........................SOLVABLE EQUATIONS AND RADICAL EXTENSIONS
CHAPTER 27..........................EPILOGUE: THE IDEA OF LIE THEORY AS A GALOIS
THEORY FOR DIFFERENTIAL EQUATIONS
