Paul B Garrett

Abstract Algebra

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• Seitenzahl: 464
• Erscheinungstermin: 11. September 2019
• Englisch
• Abmessung: 249mm x 178mm x 28mm
• Gewicht: 794g
• ISBN-13: 9780367388584
• ISBN-10: 0367388588
• Artikelnr.: 57784335

Autorenporträt

Garrett, Paul B.

Inhaltsangabe

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.