UNIVERSITEXT

By ANDREW SANCHEZ

CONTENTS CONSTRUCTIBILITY WITH RULER AND COMPASS ALGEBRAIC EXTENSIONS SIMPLE EXTENSIONS FUNDAMENTALS OF DIVISIBILITY PRIME FACTORIZATION IN POLYNOMIAL RINGS GAUSS’S THEOREM POLYNOMIAL SPLITTING FIELDS SEPARABLE EXTENSIONS GALOIS EXTENSIONS FINITE FIELDS, CYCLIC GROUPS AND ROOTS OF UNITY GROUP ACTIONS APPLICATIONS OF GALOIS THEORY TO CYCLOTOMIC FIELDS FURTHER STEPS INTO GALOIS THEORY NORM AND TRACE BINOMIAL EQUATIONS SOLVABILITY OF EQUATIONS INTEGRAL RING EXTENSIONS THE TRANSCENDENCE OF TRANSCENDENTAL FIELD EXTENSIONS HILBERT’S NULLSTELLENSATZ