Algebra - Louis Rowen

Algebra

Groups, Rings, and Fields

(Autor)

Buch | Softcover
264 Seiten
2019
CRC Press (Verlag)
978-0-367-44923-0 (ISBN)
77,30 inkl. MwSt
This book provides the traditional role of exercises in a course to provide more-or-less routine applications of the main results, for the student's edification and also as possible material for examinations. It discusses Noetherian rings and prime ideals for algebraic geometry.
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

Rowen /, Louis

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

Erscheinungsdatum
Reihe/Serie Textbooks in Mathematics
Verlagsort London
Sprache englisch
Maße 152 x 229 mm
Gewicht 453 g
Themenwelt Mathematik / Informatik Mathematik Algebra
ISBN-10 0-367-44923-4 / 0367449234
ISBN-13 978-0-367-44923-0 / 9780367449230
Zustand Neuware
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