Number Theory (Paperback)

The Foundations of Arthmetic in the Rational Number Field: Prime Decomposition. Divisibility. Congruences. The Structure of the Residue Class Ring mod m and the Reduces Residue Class Group mod m. Quadratic Residues.- The Theory of Valued Fields: The Fundamental Concepts Regarding Valuations. Arithmetic in a Discrete Valued Field. The Completion of a Valued Field. The Completion of a Discrete Valued Field. The p-adic Number Fields. The Isomorphism Types of Complete Discrete Valued Fields with Perfect Residue Class Field. Prolongation of the Discrete Valuation to a Purely Transcendental Extension. Prolongation of the Valuation of a Complete Field to a Finite Algebraic Extension. .... The Foundation of Arithmetic in Algebraic Number Fields: Relations Between the Complete System of Valuations and the Arithmetic of the Rational Number Field. Prolongation of the Complete System of Valuations to a Finite-Algebraic Extension. .....