Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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The ModularArithmetics are the images of the IntegerNumbers under group/ring HomoMorphisms. Such an operation is going to zero out some NormalSubgroup/Ideal, and these turn out to be precisely the sets of the form pZ for some integer p; the resulting group/ring is denoted Zp. To put it another way, Zp consists of the remainders {0,1,...,p-1}, so that p=0. For instance, Z3 has the following addition and multiplication tables: + 0 1 2 0 0 1 2 1 1 2 0 2 2 0 1 * 0 1 2 0 0 0 0 1 0 1 2 2 0 2 1 When p is a composite number, the factors of p are going to turn out to be ZeroDivisors. When p is prime, these don't exist, and so Zp is an IntegralDomain and in fact necessarily a field.