Algebra
Groups, Rings, and Fields
1st Edition
Published on 17. December 2019
Book
Paperback/Softback
264 pages
978-0-367-44923-0 (ISBN)
Description
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 - Cauchyis 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
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Dimensions
Height: 229 mm
Width: 152 mm
Weight
453 gr
ISBN-13
978-0-367-44923-0 (9780367449230)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
01/1995
1st Edition
A K Peters
€46.02
Article exhausted; check for reprint
Person
Rowen \, Louis
Content
Part I: Groups 1. Monoids and Groups 2. How to Divide: Lagrange's Theorem, Cosets, and an Application to Number Theory 3. Cauchy's Theorem: How to Show a Number is Greater than 1 4. Introduction to the Classification of Groups: Homomorphisms, Isomorphisms, and Invariants 5. Normal Subgroups- the Building Blocks of the Structure Theory 6. Classifying Groups- Cyclic Groups and Direct Products 7. Finite Abelian Groups 8. Generators and Relations 9. When is a Group a Group? (Cayley's Theorem) 10. Recounting: Conjugacy Classes and the Class Formula 11. Sylow Subgroups: A New Invariant 12. Solvable Groups: What Could Be Simpler? Part II: Rings and Polynomials 14. An Introduction to Rings 15. The Structure Theory of Rings 16. The Field of Fractions- a Study in Generalization 17. Principal Ideal Domains: Induction without Numbers 18. Roots of Polynomials 19. (Optional) Applications: Famous Results from Number Theory 20. Irreducible Polynomials Part III: Fields 21. Field Extensions: Creating Roots of Polynomials 22. The Problems of Antiquity 23. Adjoining Roots to Polynomials: Splitting 24. Finite Fields 25. The Galois Correspondence 26. Applications of the Galois Correspondence 27. Solving Equations by Radicals