Introduction to abstract algebra: solutions manual

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 the basic structures of abstractalgebra: 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 are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.The Fourth Edition features important concepts as well as specialized topics, including:The treatment of nilpotent groups, including the Frattini and Fitting subgroupsSymmetric polynomialsThe proof of the fundamental theorem of algebra usingsymmetric polynomialsThe proof of Wedderburn's theorem on finite division ringsThe proof of the Wedderburn-Artin theoremThroughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics. INDICE: 0 Preliminaries 10.1 Proofs / 10.2 Sets / 20.3 Mappings / 30.4 Equivalences / 41 Integers and Permutations 61.1 Induction / 61.2 Divisors and Prime Factorization / 81.3 Integers Modulo1.4 Permutations / 132 Groups 172.1 Binary Operations / 172.2 Groups / 192.3 Subgroups / 212.4 Cyclic Groups and theOrder of an Element / 242.5 Homomorphisms and Isomorphisms / 282.6 Cosets andLagrange's Theorem / 302.7 Groups of Motions and Symmetries / 322.8 Normal Subgroups / 342.9 Factor Groups / 362.10 The Isomorphism Theorem / 382.11 An Application to Binary Linear Codes / 433 Rings 473.1 Examples and Basic Properties / 473.2 Integral Domains and Fields / 523.3 Ideals and Factor Rings / 553.4 Homomorphisms / 593.5 Ordered Integral Domains / 624 Polynomials 644.1 Polynomials / 644.2 Factorization of Polynomials over a Field / 674.3 Factor Rings ofPolynomials over a Field / 704.4 Partial Fractions / 764.5 Symmetric Polynomials / 765 Factorization in Integral Domains 815.1 Irreducibles and Unique Factorization / 815.2 Principal Ideal Domains / 846 Fields 886.1 Vector Spaces / 886.2 Algebraic Extensions / 906.3 Splitting Fields / 946.4 Finite Fields / 966.5 Geometric Constructions / 986.7 An Application to Cyclic and BCH Codes / 997 Modules over Principal Ideal Domains 1027.1 Modules / 1027.2 Modules over a Principal Ideal Domain / 1058 p-Groups and the Sylow Theorems8.1 Products and Factors / 1088.2 Cauchy’s Theorem / 1118.3 Group Actions / 1148.4 The Sylow Theorems / 1168.5 Semidirect Products / 1188.6 An Application to Combinatorics /1199 Series of Subgroups 1229.1 The Jordan-H¨older Theorem / 1229.2 Solvable Groups / 1249.3 Nilpotent Groups / 12710 Galois Theory 13010.1 Galois Groups and Separability / 13010.2 The Main Theorem of Galois Theory / 13410.3 Insolvability of Polynomials / 13810.4 Cyclotomic Polynomials and Wedderburn's Theorem / 14011 Finiteness Conditions for Rings and Modules 14211.1 Wedderburn's Theorem / 14211.2 The Wedderburn-Artin Theorem / 143Appendices 147Appendix A: Complex Numbers / 147Appendix B: Matrix Arithmetic / 148Appendix C: Zorn's Lemma / 149

• ISBN: 978-1-118-28815-3
• Editorial: John Wiley & Sons
• Encuadernacion: Rústica
• Páginas: 160
• Fecha Publicación: 01/06/2012
• Nº Volúmenes: 1
• Idioma: Inglés