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
- Cauchyis 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
General
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