Algebraic Number Theory Problems and Solutions

These are homework problems and my solutions for an introductory algebraic number theory class I took in Fall 2006. The text for the class was Algebraic Number Theory by J.S. Milne, available (for free) here.
Caveat lector: I make no claim to the correctness of the solutions here, use them at your own risk.

• Sums of squares, Euclidean domains, PIDs, primes vs irreducibles: Problems, Solutions
• Integral closure, rings of integers: Problems, Solutions
• Field extensions, discriminants, integral basis: Problems, Solutions
• Orders, Dedekind domains: Problems, Solutions
• Ideal classes, more Dedekind domains: Problems, Solutions
• Ramification: Problems, Solutions
• Class numbers, unramified/ramified extensions: Problems, Solutions
• Lattices, Minkowski's Theorem: Problems, Solutions
• Dirichlet's Units Theorem, quadratic fields, cubic fields: Problems, Solutions
• More on units: Problems, Solutions

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Last updated: 5 December, 2006