In Atiyah-Macdonald, the Going-Down Theorem (listed as Theorem 5.16) assumes the integral extension to be a domain, which is due to the usage of a lemma (listed as Proposition 5.15). However, it seems to me nowhere in the proofs of both theorems used this assumption, so I wonder if it can be removed.
2026-04-13 12:34:09.1776083649
Hypothesis of the Going-Down Theorem
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