04240nam 2200601 450 991046162820332120200520144314.01-118-34789-71-118-34787-0(CKB)2670000000177454(EBL)843673(OCoLC)787842658(SSID)ssj0000662918(PQKBManifestationID)11400556(PQKBTitleCode)TC0000662918(PQKBWorkID)10739195(PQKB)11536771(MiAaPQ)EBC843673(Au-PeEL)EBL843673(CaPaEBR)ebr10915835(CaONFJC)MIL639070(EXLCZ)99267000000017745420140902h20122012 uy 0engur|n|---|||||txtccrSolutions accompany manual introduction to abstract algebra /W. Keith NicholsonFourth edition.Hoboken, New Jersey :Wiley,2012.©20121 online resource (233 p.)Description based upon print version of record.1-322-07819-X 1-118-28815-7 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: Rings3.1 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 Constructions6.7 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 Polynomials10.4 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 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 aAlgebra, AbstractElectronic books.Algebra, Abstract.512/.02Nicholson W. Keith104483MiAaPQMiAaPQMiAaPQBOOK9910461628203321Solutions accompany manual introduction to abstract algebra2070505UNINA