Algebra. Algebra is the deep study of operations like multiplication, which turn two objects into a single object. This proof lies in the area of ring theory, which is concerned with the interaction of two such operations whose interaction is analogous to that of addition and multiplication. However, the “addition” and “multiplication” operations themselves are allowed to be rather exotic. For instance, this proof discusses a basic property of the “nilradical”. This is the set of nonzero elements, which have the counterintuitive property that, when multiplied by themself enough times, they give an answer of zero!
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