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Autore: | Nicholson W. Keith |
Titolo: | Solutions accompany manual introduction to abstract algebra / / W. Keith Nicholson |
Pubblicazione: | Hoboken, New Jersey : , : Wiley, , 2012 |
©2012 | |
Edizione: | Fourth edition. |
Descrizione fisica: | 1 online resource (233 p.) |
Disciplina: | 512/.02 |
Soggetto topico: | Algebra, Abstract |
Soggetto genere / forma: | Electronic books. |
Note generali: | Description based upon print version of record. |
Nota di contenuto: | Cover; Title Page; Copyright; 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; 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 Subgroups; 2.9 Factor Groups; 2.10 The Isomorphism Theorem; 2.11 An Application to Binary Linear Codes; Chapter 3: Rings |
3.1 Examples and Basic Properties3.2 Integral Domains and Fields; 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; Chapter 5: Factorization in Integral Domains; 5.1 Irreducibles and Unique Factorization; 5.2 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 | |
6.7 An Application to Cyclic and BCH CodesChapter 7: Modules over Principal Ideal Domains; 7.1 Modules; 7.2 Modules over a Principal Ideal Domain; 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 Subgroups; 9.1 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 TheoremChapter 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 Arithmetic; Appendix C: Zorn's Lemma | |
Sommario/riassunto: | Praise for the Third Edition "". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .""-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures a |
Titolo autorizzato: | Solutions accompany manual introduction to abstract algebra |
ISBN: | 1-118-34789-7 |
1-118-34787-0 | |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910461628203321 |
Lo trovi qui: | Univ. Federico II |
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