Affine scheme
An affine scheme Χ over a field K in n variables, x1,...,xn with m polynomials, p1,...,pm in these variables over K is a functor from the category of commutative K-algebras to sets characterized by Χ(A)={(x1,...,xn)|p1=...=pm=0}.Given A, a commutative unital associative algebra over K, we can define an affine scheme as follows: ΧA(B)=Morph(A,B) over the category of commutative associative unital K-algebras (a representable functor).
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