A First Course in Algebra and Number Theory - ISBN:0127431500

A First Course in Algebra and Number Theory

Date: 21 April 2011, 11:39

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Table of Contents
I. Elementary Number Theory
1-1. DIVISIBILITY 2
1-2. THE DIVISION ALGORITHM 6
1-3. THE GREATEST COMMON DIVISOR 13
1-4. UNIQUE FACTORIZATION 21
1-5. A CONVENIENT NOTATION 28
1-6. LINEAR DIOPHANTINE EQUATIONS 42
1-7. CONGRUENCE 50
1-8. RADIX REPRESENTATION 64
MISCELLANEOUS PROBLEMS 83
II. Rings and Domains
2-1. RINGS: ELEMENTARY PROPERTIES 91
2-2. EXAMPLES 104
2-3. ORDERED AND WELL-ORDERED DOMAINS 138
2-4. COMPUTATION RULES 160
2-5. CHARACTERIZATION OF THE INTEGERS 174
MISCELLANEOUS PROBLEMS 199
III. Congruences and Polynomials
3-1. LINEAR CONGRUENCES
3-2. UNITS AND FIELDS
3-3. POLYNOMIALS AND POLYNOMIAL FUNCTIONS
3-4. FACTORIZATION IN F[x]
3-5. ROOTS OF POLYNOMIALS
3-6. SOL YING POLYNOMIALS IN Zm[X]
3-7. QUADRATIC RECIPROCITY
MISCELLANEOUS PROBLEMS
IV. Groups
BASIC FACTS AND EXAMPLES
SUBGROUPS AND COSETS
CYCLIC GROUPS
NORMAL SUBGROUPS; FACTOR GROUPS; HOMOMORPHISMS
PERMUTATION GROUPS
THE GROUP Zm
MISCELLANEOUS PROBLEMS
Selected Answers and Comment
Subject Index

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