In twelve chapters, the author explains the main topics in abstract algebra with many useful examples.
An Introduction to Abstract Algebra
The first two chapters introduce fundamental concepts set, class, properties of integers, GCD, Euclidean algorithm, the fundamental theorem of arithmetics. The concept of a group is explored in Chapters 3, 4, 5 and 9. The exposition follows a historical development, and the author uses the group of permutations as a motivating example.
Group actions are used to investigate the group structure. Algebraic structures with two binary operations are introduced in Chapter 6: rings, Euclidean domains, roots of polynomials, and splitting fields.
You don't smell human...
Vector spaces are used in many applications: they are discussed in a separate chapter with many examples. Chapters 10 and 11 contain a description of fields and Galois theory, with applications to orthogonal latin squares, Steiner systems and the solvability of equations by radicals.
Math 403 - Introduction to Abstract Algebra
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