Algebraic Number Theory: Notes by Anwar Khan

CONTENTS OR SUMMARY:

• Algebraic Number Theory \dotfill 1
• Diophantine Equation and Fermat’s Conjecture \dotfill 2
• Polynomial over the Rational \dotfill 10
• Degree of Polynomial \dotfill 10
• Monic Polynomial
• Division of Polynomial
• Irreducible Polynomial
• Division Algorithm
• Greatest Common Divisor
• Algebraic Number
• Degree of Algebraic Number
• Minimal Polynomial
• Conjugates of an Algebraic Number
• Primitive Polynomial
• Product of Polynomial
• Symmetric Polynomial
• Alternative Statement
• Primitive Element
• Eisenstein’s Irreducibility Eriterion

• Algebraic Integer
• The Determinant
• Euclidian Domain
• Quadratic Field
• Square Free Rational Integer
• Prime
• Ideal
• Principal Ideal
• Congruence of an Ideal
• Norm f an Ideal
• Decrement
• Units and Primes in $R$
• Unique Factorization Domain
• Arithmetic of an Ideal
• Prime Ideal
• Equivalent Ideal
• Cyclotomic Field KP
• Pure Cubic Field