Algebra Groups, Rings, and Fields Free Download

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