Louis Rowen

Algebra

Groups, Rings, and Fields

• Broschiertes Buch

Produktbeschreibung

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 - Cauchyís 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

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Produktdetails

• Verlag: A K Peters/CRC Press
• Seitenzahl: 264
• Erscheinungstermin: 17. Dezember 2019
• Englisch
• Abmessung: 229mm x 152mm x 14mm
• Gewicht: 388g
• ISBN-13: 9780367449230
• ISBN-10: 0367449234
• Artikelnr.: 58503017

Autorenporträt

Rowen \, Louis

Inhaltsangabe

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