Let $A$ be a domain, not necessarily noetherian or normal, let $X = {\rm Spec}(A)$ and let $U\subseteq X$ be the complement of a prime divisor of $X$. Is it possible that $\mathcal O_U(U) = \mathcal O_X(X)$?
Complement of a divisor in an affine scheme
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algebraic-geometry
commutative-algebra
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2What is a prime divisor for you? I guess just a height one prime? – 2017-02-15