Algebra

Groups, Rings, and Fields

Louis Rowen

• Publisher: A K Peters/CRC Press
• Year: 2018
• ISBN:
  9781439863527
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• Table of Principal Notation
• Prerequisites
• PART I—GROUPS
• PART II—RINGS AND POLYNOMIALS
• PART III—FIELDS
• Appendix A . Transcendental Numbers: e and π
• Appendix B. Skew Field Theory
• Index