Neither ask the exact same question. The first that you have cited asks something completely different about a similar topic: it asks for clarification of the notation $\mathbb{C}(x_1, x_2, ...)$ for a quotient field over infinitely many indeterminates. The second question that you cited requires that the example given be a non-Noetherian UFD, not just a ring that doesn't satisfy the ascending chain condition. So, it should not be closed at all, as stated previously. —
Will Byrne 10 hours ago