Example
Consider the affine line A1(k) = Spec(k) over a field k. If k is algebraically closed, there are exactly two types of prime ideals, namely
- (t − a), a ∈ k
- (0), the zero-ideal.
The residue fields are
- , the function field over k in one variable.
If k is not algebraically closed, then more types arise, for example if k = R, then the prime ideal (x2 + 1) has residue field isomorphic to C.
Read more about this topic: Residue Field
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