Polynomial and Rational Functions on a Variety
One of the unifying themes of modern mathematics is that in order to understand any class of mathematical objects, one should also study mappings between those objects, and especially the mappings which preserve some property of interest. For instance, in linear algebra after studying vector spaces, you also studied the properties of linear mappings between vector spaces (mappings that preserve the vector space operations of sum and scalar product).
KeywordsRational Function Variety Versus Commutative Ring Integral Domain Ring Homomorphism
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