دانلود کتاب A First Course in Abstract Algebra, 7th Edition

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1 Introduction and Examples............................................... 24 2 Binary Operations....................................................... 33 3 Isomorphic Binary Structures............................................ 41 4 Groups.................................................................. 49 5 Subgroups............................................................... 62 6 Cyclic Groups........................................................... 72 7 Generating Sets and Cayley Digraphs..................................... 81 8 Groups of Permutations.................................................. 88 9 Orbits, Cycles, and the Alternating Groups..............................100 10 Cosets and the Theorem of Lagrange.....................................109 11 Direct Products and Finitely Generated Abelian Groups..................117 12 Plane Isometries.......................................................127 13 Homomorphisms..........................................................138 14 Factor Groups..........................................................148 15 Factor-Group Computations and Simple Groups............................157 16 Group Action on a Set..................................................167 17 Applications of G-Sets to Counting.....................................174 18 Rings and Fields.......................................................180 19 Integral Domains.......................................................190 20 Fermat's and Euler's Theorems..........................................197 21 The Field of Quotients of an Integral Domain...........................203 22 Rings of Polynomials...................................................211 23 Factorization of Polynomials over a Field..............................222 24 Noncommutative Examples................................................233 25 Ordered Rings and Fields...............................................240 26 Homomorphisms and Factor Rings.........................................250 27 Prime and Maximal Ideals...............................................258 28 Grobner Bases for Ideals...............................................267 29 Introduction to Extension Fields.......................................278 30 Vector Spaces..........................................................287 31 Algebraic Extensions...................................................296 32 Geometric Constructions................................................306 33 Finite Fields..........................................................313 34 Isomorphism Theorems...................................................320 35 Series of Groups.......................................................324 36 Sylow Theorems.........................................................334 37 Applications of the Sylow Theory.......................................340 38 Free Abelian Groups....................................................346 39 Free Groups............................................................354 40 Group Presentations....................................................359 41 Simplicial Complexes and Homology Groups...............................368 42 Computations of Homology Groups........................................376 43 More Homology Computations and Applications............................384 44 Homological Algebra....................................................392 45 Unique Factorization Domains...........................................402 46 Euclidean Domains......................................................414 47 Gaussian Integers and Multiplicative Nonns.............................420 48 Automorphisms of Fields................................................428 49 The Isomorphism Extension Theorem......................................437 50 Splitting Fields.......................................................444 51 Separable Extensions...................................................449 52 Totally Inseparable Extensions.........................................457 53 Galois Theory..........................................................461 54 Illustrations of Galois Theory.........................................470 55 Cyclotomic Extensions..................................................477 56 Insolvability of the Quintic...........................................483 Appendix: Matrix Algebra..................................................490 Bibliography..............................................................496 Notations.................................................................500 Answers to Odd-Numbered Exercises Not Asking for Definitions or Proofs....504 Index.....................................................................526