Fields and Galois Theory

2005. Corr. 2. Printing 2007 Auflage 2005
ISBN: 978-1-85233-986-9
Verlag: Springer

Buch, Englisch, 226 Seiten, Format (B × H): 179 mm x 238 mm, Gewicht: 397 g

Reihe: Springer Undergraduate Mathematics Series

This book provides a gentle introduction to this popular subject. Assuming a background of a first course in abstract algebra, the book covers rings, ideals, quotients and homomorphisms, introduces polynomials, field extensions and splitting fields, gives a description of finite fields, and includes a brief account of the use of such fields in coding theory. It provides a readable, "student-friendly" introduction that takes a more "natural" approach to its subject (compared to the more formal introductions by Stewart and Garling), and that features clear explanations and plenty of worked examples and exercises - with full solutions – to encourage independent study.

Zielgruppe

Advanced undergraduate and beginning graduate students

Autoren/Hrsg.

Howie, John M

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Elementare Algebra
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Rings and Fields.- Integral Domains and Polynomials.- Field Extensions.- Applications to Geometry.- Splitting Fields.- Finite Fields.- The Galois Group.- Equations and Groups.- Some Group Theory.- Groups and Equations.- Regular Polygons.- Solutions.