| instructor's preface vii. student's preface xi dependence chart xiii 0 sets and relations 1 ⅰ groups and subgroups 1 introduction and examples 11 2 binary operations 20 3 isomorphic binary structures 28 4 groups 36 5 subgroups 49 6 cyclic groups 59 7 generating sets and cayley digraphs 68 ⅱ permutations, cosets, and direct products 8 groups of permutations 75 9 orbits, cycles, and the alternating groups 87 10 cosets and the theorem of lagrange 96 11 direct products and finitely generated abelian groups 104 12 planeisometries 114 ⅲ homomorphisms and factor groups 13 homomorphisms 125 .14 factor groups 135 15 factor-group computations and simple groups 144 16 group action on a set 154 17 applications of g-sets to counting 161 ⅳ rings and fields 18 rings and fields 167 19 integral domains 177 20 fermat's and euler's theorems 184 21 the field of quotients of an integral domain 190 22 rings of polynomials 198 23 factorization of polynomials over a field 209 24 noncommutative examples 220 25 ordered rings and fields 227 ⅴ ideals and factor rings 26 homomorphisms and factor rings 237 27 prime and maximal ideals 245 28 gr6bner bases for ideals 254 ⅵ extension fields 29 introduction to extension fields 265 30 vector spaces 274 31 algebraic extensions ..283 32 geometric constructions 293 33 finite fields 300 ⅶ advanced group theory 34 isomorphism theorems 307 35 series of groups 311 36 sylow theorems 321 37 applications of the sylow theory 327 38 free abelian groups 333 39 free groups 341 40 group presentations 346 ⅷ groups in topology 41 simplicial complexes and homology groups 355 42 computations of homology groups 363 43 more homology computations and applications 371 44 homological algebra 379 ⅸ factorization 45 unique factorization domains 389 46 euclidean domains 401 47 gaussian integers and multiplicative norms 407 ⅹ automorphisms and galois theory 415 48 automorphisms of fields 415 49 the isomorphism extension theorem 424 50 splitting fields 431 51 separable extensions 436 52 totally inseparable extensions 444 53 galois theory 448 54 illustrations of galois theory 457 55 cyclotomic extensions 464 56 insolvability of the quintic 470 appendix: matrix algebra 477 bibliography 483 notations 487 answers to odd-numbered exercises not asking for definitions or proofs 491 index ...513 |
内容加载中，请稍后...
商品评论（0条）