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Introduction to abstract algebra /
Praise for the Third Edition". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."--Zentralblatt MATHThe Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
John Wiley & Sons,
©2012.
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| Edición: | 4th ed. |
| Temas: | |
| Acceso en línea: | Texto completo (Requiere registro previo con correo institucional) |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Preface; Acknowledgments; Notation Used in the Text; A Sketch of the History of Algebra to 1929; Chapter 0: Preliminaries; 0.1 Proofs; 0.2 Sets; 0.3 Mappings; 0.4 Equivalences; Chapter 1: Integers and Permutations; 1.1 Induction; 1.2 Divisors and Prime Factorization; 1.3 Integers Modulo n; 1.4 Permutations; 1.5 An Application to Cryptography; Chapter 2: Groups; 2.1 Binary Operations; 2.2 Groups; 2.3 Subgroups; 2.4 Cyclic Groups and the Order of an Element; 2.5 Homomorphisms and Isomorphisms; 2.6 Cosets and Lagrange's Theorem; 2.7 Groups of Motions and Symmetries.
- 2.8 Normal Subgroups2.9 Factor Groups; 2.10 The Isomorphism Theorem; 2.11 An Application to Binary Linear Codes; Chapter 3: Rings; 3.1 Examples and Basic Properties; 3.2 Integral Domains and Fields; 3.2 Exercises; 3.3 Ideals and Factor Rings; 3.4 Homomorphisms; 3.5 Ordered Integral Domains; Chapter 4: Polynomials; 4.1 Polynomials; 4.2 Factorization of Polynomials over a Field; 4.3 Factor Rings of Polynomials over a Field; 4.4 Partial Fractions; 4.5 Symmetric Polynomials; 4.6 Formal Construction of Polynomials; Chapter 5: Factorization in Integral Domains.
- 5.1 Irreducibles and Unique Factorization5.2 Principal Ideal Domains; Chapter 6: Fields; 6.1 Vector Spaces; 6.2 Algebraic Extensions; 6.3 Splitting Fields; 6.4 Finite Fields; 6.5 Geometric Constructions; 6.6 The Fundamental Theorem of Algebra; 6.7 An Application to Cyclic and BCH Codes; Chapter 7: Modules over Principal Ideal Domains; 7.1 Modules; 7.2 Modules Over a PID; Chapter 8: p-Groups and the Sylow Theorems; 8.1 Products and Factors; 8.2 Cauchy's Theorem; 8.3 Group Actions; 8.4 The Sylow Theorems; 8.5 Semidirect Products; 8.6 An Application to Combinatorics.
- Chapter 9: Series of Subgroups9.1 The Jordan-Hölder Theorem; 9.2 Solvable Groups; 9.3 Nilpotent Groups; Chapter 10: Galois Theory; 10.1 Galois Groups and Separability; 10.2 The Main Theorem of Galois Theory; 10.3 Insolvability of Polynomials; 10.4 Cyclotomic Polynomials and Wedderburn's Theorem; Chapter 11: Finiteness Conditions for Rings and Modules; 11.1 Wedderburn's Theorem; 11.2 The Wedderburn-Artin Theorem; Appendices; Appendix A Complex Numbers; Appendix B Matrix Algebra; Appendix C Zorn's Lemma; Appendix D Proof of the Recursion Theorem; Bibliography; Selected Answers; Index.