I'm not sure whether this is non-trivial or not, but do there exist simple examples of an affine scheme X having an open affine subscheme U which is not principal in X? By a principal open of X = Spec A, I mean anything of the form D(f) = {P in Spec A : f is not in P}, where f is an element of A.
Open affine subscheme of affine scheme which is not principal
Wanderer
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