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Tag Archives: algebraic number theory
Topics in Commutative Rings: Unique Factorisation (3)
Example 1: The Gaussian Integers Z[i] Let’s pick the norm function N : Z[i]{0} → N where N(a+bi) = (a+bi)(a–bi) = a2+b2. We know that N is a multiplicative function, i.e. N(r)N(s) = N(rs). Instead of checking this by brute force, we write N(x) = x·xc, where (a+bi)c = abi is the conjugate of a+bi. It’s easy to … Continue reading