A Book of Abstract Algebra

CONTENTS
PREFACE
CHAPTERS
	CHAPTER 1: WHY ABSTRACT ALGEBRA?
	CHAPTER 2: OPERATIONS
	CHAPTER 3: THE DEFINITION OF GROUPS
	CHAPTER 4: ELEMENTARY PROPERTIES OF GROUPS
	CHAPTER 5: SUBGROUPS
	CHAPTER 6: FUNCTIONS
	CHAPTER 7: GROUPS OF PERMUTATIONS
	CHAPTER 8: PERMUTATIONS OF A FINITE SET
	CHAPTER 9: ISOMORPHISM
	CHAPTER 10: ORDER OF GROUP ELEMENTS
	CHAPTER 11: CYCLIC GROUPS
	CHAPTER 12: PARTITIONS AND EQUIVALENCE
RELATIONS
	CHAPTER 13: COUNTING COSETS
	CHAPTER 14: HOMOMORPHISMS
	CHAPTER 15: QUOTIENT GROUPS
	CHAPTER 16: THE FUNDAMENTAL HOMOMORPHISM
THEOREM
	CHAPTER 17: RINGS: DEFINITIONS AND
ELEMENTARY PROPERTIES
	CHAPTER 18: IDEALS AND HOMOMORPHISMS
	CHAPTER 19: QUOTIENT RINGS
	CHAPTER 20: INTEGRAL DOMAINS
	CHAPTER 21: THE INTEGERS
	CHAPTER 22: FACTORING INTO PRIMES
	CHAPTER 23: ELEMENTS OF NUMBER THEORY (OPTIONAL)
	CHAPTER 24: RINGS OF POLYNOMIALS
	CHAPTER 25: FACTORING POLYNOMIALS
	CHAPTER 26: SUBSTITUTI ON IN POLYNOMIALS
	CHAPTER 27: EXTENSIONS OF FIELDS
	CHAPTER 28: VECTOR SPACES
	CHAPTER 29: DEGREES OF FIELD EXTENSIONS
	CHAPTER 30: RULER AND COMPASS
	CHAPTER 31: GALOIS THEORY: PREAMBLE
	CHAPTER 32: GALOIS THEORY: THE HEART OF
THE MATTER
	CHAPTER 33: SOLVING EQUATIONS BY RADICALS
APPENDIX
	APPENDIX A: REVIEW OF SET THEORY
	APPENDIX B: REVIEW OF THE INTEGERS
	APPENDIX C: REVIEW OF MATHEMATICAL INDUCTION
ANSWERS TO SELECTED EXERCISES
	CHAPTER 2
	CHAPTER 3
	CHAPTER 4
	CHAPTER 5
	CHAPTER 6
	CHAPTER 7,8
	CHAPTER 9
	CHAPTER 10
	CHAPTER 11
	CHAPTER 12,13
	CHAPTER 14
	CHAPTER 15,16
	CHAPTER 17
	CHAPTER 18, 19, 20
	CHAPTER 21, 22
	CHAPTER 23
	CHAPTER 24
	CHAPTER 25, 26
	CHAPTER 27
	CHAPTER 28
	CHAPTER 29
	CHAPTER 30, 31
	CHAPTER 32, 33
INDEX