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Oct 10, 2019 at 14:45 history edited Pierre-Yves Gaillard CC BY-SA 4.0
typo
Oct 10, 2019 at 14:45 vote accept Pierre-Yves Gaillard
Oct 10, 2019 at 14:03 comment added YCor @Pierre-YvesGaillard oh thanks. Indeed Eric's example is immediately adaptable to answer the question.
Oct 10, 2019 at 12:45 answer added darx timeline score: 18
Oct 10, 2019 at 10:42 comment added Pierre-Yves Gaillard @YCor - I hope you saw Angelo's comment. (At the end of the question I mentioned Eric Wofsey' example of a non-surjective epimorphic endomorphism of a noetherian ring.)
Oct 10, 2019 at 7:51 comment added Angelo The embedding $\mathbb{Z} \times \mathbb{Z} \subseteq \mathbb{Z} \times \mathbb{Q}$ is such an example.
Oct 10, 2019 at 7:17 comment added YCor Do you have an example of a non-surjective epimorphism $A\to B$ of noetherian rings with $A,B$ with the Krull dimension of $A$ $\le$ that of $B$? (Say, with finite Krull dimension— otherwise the Krull dimension should be defined as an ordinal, namely as $\mathrm{Kdim}(A)=\sup(\mathrm{Kdim}(A/P)+1)$ for $A\neq 0$, where $P$ ranges over non-minimal prime ideals and $\sup\emptyset=0$.)
Oct 8, 2019 at 12:51 history edited Pierre-Yves Gaillard CC BY-SA 4.0
typos caught by Steven Landsburg
Oct 8, 2019 at 12:32 history asked Pierre-Yves Gaillard CC BY-SA 4.0