| Description |
1 online resource (264 pages) |
| Contents |
Part, PART I--GROUPS -- chapter 1 Monoids and Groups -- chapter 2 How to Divide: Lagrange's Theorem, Cosets, and an Application to Number Theory -- chapter 3 Cauchy's Theorem: How to Show a Number Is Greater Than 1 -- chapter 4 Introduction to the Classification of Groups: Homomorphisms, Isomorphisms, and Invariants -- chapter 5 Normal Subgroups--The Building Blocks of the Structure Theory -- chapter 6 Classifying Groups--Cyclic Groups and Direct Products -- chapter 7 Finite Abelian Groups -- chapter 8 Generators and Relations -- chapter 9 When Is a Group a Group? (Cayley's Theorem) -- chapter 10 Recounting: Conjugacy Classes and the Class Formula -- chapter 11 Sylow Subgroups: A New Invariant -- chapter 12 Solvable Groups: W hat Could Be Simpler? -- part, PART II--RINGS AND POLYNOMIALS -- chapter 13 An Introduction to Rings -- chapter 14 The Structure Theory of Rings -- chapter 15 The Field of Fractions--A Study in Generalization -- chapter 16 Polynomials and Euclidean Domains -- chapter 17 Principal Ideal Domains: Induction without Numbers -- chapter 18 Roots of Polynomials -- chapter 19 (Optional) Applications: Famous Results from Number Theory -- chapter 20 Irreducible Polynomials -- chapter Historical Background -- chapter 21 Field Extensions: Creating Roots of Polynomials -- chapter 22 The Problems of Antiquity -- chapter 23 Adjoining Roots to Polynomials: Splitting Fields -- chapter 24 Finite Fields -- chapter 25 The Galois Correspondence -- chapter 26 Applications of the Galois Correspondence -- chapter 27 Solving Equations by Radicals |
| Summary |
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 - Cauchyiś 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 |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Algebra.
|
|
Anneaux (algeb̀re)
|
|
algebra.
|
|
Algebra
|
| Form |
Electronic book
|
| ISBN |
9781439863527 |
|
1439863520 |
|
