文档介绍：To my wife
Marganit
and our two wonderful kids,
Danny and Ella,
whom I love very much
Contents
Second Printing . .................................. viii
Preface....................................... ix
Etymology..................................... xii
Special Notation .................................. xiii
Chapter 1 Things Past ............................ 1
. Some Number Theory ............................. 1
................................. 15
. Some Set Theory . . ............................. 25
Chapter 2 Groups I .............................. 39
. Introduction .................................. 39
.................................. 40
. Groups . . . .................................. 51
. Lagrange’s Theorem ............................. 62
............................... 73
. Quotient Groups . . . ............................. 82
................................. 96
Chapter mutative Rings I ..................... 116
. Introduction .................................. 116
. First Properties . . . ............................. 116
. Polynomials .................................. 126
.......................... 131
............................... 143
. Euclidean Rings . . . ............................. 151
. Linear Algebra . . . ............................. 158
Vector Spaces . . . ............................. 159
Linear Transformations . . . ........................ 171
....................... 182
v
vi Contents
Chapter 4 Fields ................................ 198
. Insolvability of the Quintic . . ........................ 198
Formulas and Solvability by Radicals ................... 206
Translation into Group Theory ....................... 210
. Fundamental Theorem of Galois Theory ................... 218
Chapter 5 Groups I