| Joseph J．Rotman是美国伊利诺伊大学Urbana-Champaign分校数学系教授，他著有多部数学方面的书，其中包括《Advanced Modern Algebra》、《Galois Theory》等。 .. << 查看详细 |
| preface to the first edition preface to the second edition chapter 1 number theory 1.1. induction 1.2. binomial coefficients 1.3. greatest common divisors 1.4. the fundamental theorem of arithmetic 1.5. congruences 1.6. dates and days chapter 2 groups i 2.1. functions 2.2. permutations 2.3. groups symmetry 2.4. lagrange's theorem 2.5. homomorphisms 2.6. quotient groups 2.7. group actions 2.8. counting with groups chapter 3 commutative rings i . 3.1. first properties 3.2. fields 3.3. polynomials 3.4. homomorphisms 3.5. greatest common divisors euclidean rings 3.6. unique factorization 3.7. irreducibility 3.8. quotient rings and finite fields 3.9. officers, fertilizer, and a line at infinity chapter 4 goodies 4.1. linear algebra vector spaces linear transformations applications to fields 4.2. euclidean constructions 4.3. classical formulas 4.4. insolvability of the general quintic formulas and solvability by radicals translation into group theory 4.5. epilog chapter 5 groups ii 5.1. finite abelian groups 5.2. the sylow theorems 5.3. the jordan-htlder theorem 5.4. presentations chapter 6 commutauve rings ii 6.1. prime ideals and maximal ideals 6.2. unique factorization 6.3. noetherian rings 6.4. varieties 6.5. grtbner bases generalized division algorithm grtbner bases hints to exercises bibliography index |
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