Abstract Algebra

ISBN-13: 9780367388584 / Angielski / Miękka / 2019 / 464 str.

Paul B. Garrett

Opis

In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, this text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material.

Spis treści

Preface. Introduction. The Integers. Groups I. The Players: Rings, Fields. Commutative Rings I. Linear Algebra I: Dimension. Fields I. Some Irreducible Polynomials. Cyclotomic Polynomials. Finite Fields. Modules over PIDs. Finitely Generated Modules. Polynomials over UFDs. Symmetric Groups. Naive Set Theory. Symmetric Polynomials. Eisenstein's Criterion. Vandermonde Determinants. Cyclotomic Polynomials II. Roots of Unity. Cyclotomic III. Primes in Arithmetic Progressions. Galois Theory. Solving Equations by Radicals. Eigenvectors, Spectral Theorems. Duals, Naturality, Bilinear Forms. Determinants I. Tensor Products. Exterior Powers. Index.

O autorze

Garrett, Paul B.