Tag Archives: gaussian integers

Topics in Commutative Rings: Unique Factorisation (3)

Posted on November 7, 2012 by

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 = a-bi is the conjugate of a+bi. It’s easy to … Continue reading →

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Introduction to Ring Theory (3)

Posted on October 20, 2012 by

Ideals and Ring Quotients Suppose I is a subgroup of (R, +). Since + is abelian, I is automatically a normal subgroup and we get the group quotient (R/I, +). One asks when we can define the product operation on R/I. To be specific, each … Continue reading →

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