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Apr 15, 2021 at 14:05 vote accept Joël
Mar 5, 2021 at 4:34 vote accept Joël
Apr 15, 2021 at 14:05
Feb 26, 2021 at 1:39 comment added Hailong Dao @Joël: by the way, it might be worth adding the tag "semigrous-and-monoids" as people in that community may have thought about this question.
Feb 25, 2021 at 22:00 comment added Hailong Dao @Joël: a reduction of $I$ is an ideal inside $I$ that has the same integral closure. A minimal reduction is a reduction minimal w.r.t inclusion. For ideals of finite colength in a local ring $A$ with infinite residue field, they exist and can be generated by $\dim A$ elements. You can find discussion of them in the book "Integral Closure..." by Huneke-Swanson, I think it is available freely and legally online.
Feb 25, 2021 at 21:52 comment added Joël Thanks a lot, this is very helpful. I am not sure I understand your proof of 2. What is a "minimal reduction" of $I$?
Feb 25, 2021 at 0:33 history edited Hailong Dao CC BY-SA 4.0
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Feb 25, 2021 at 0:14 history answered Hailong Dao CC BY-SA 4.0