Let F be a field, and let S be any subset of F x F x
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Let F be a field, and let S be any subset of F x F x • • • x F for n factors. Show that the set Ns of all f(x1, • • •, Xn) ∈ F[x1, • • •, xn]that have every element (a1, •·•,an) of S as a zero is an ideal in F[x1 • • • , xn]. This is of importance in algebraic geometry.
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If fx 1 x n and gx 1 x n both have every element of S as a zero then so do their ...View the full answer
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