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feat(RingTheory/Ideal/GoingUp): a prime ideal is minimal over the image of its preimage#39672

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feat(RingTheory/Ideal/GoingUp): a prime ideal is minimal over the image of its preimage#39672
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@tb65536 tb65536 commented May 21, 2026

This PR proves that if A/R is integral and if I is a prime ideal of A, then I is a minimal prime over the image of its preimage in R.


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@tb65536 tb65536 added awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. t-algebra Algebra (groups, rings, fields, etc) t-ring-theory Ring theory labels May 21, 2026
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PR summary 77a248fac3

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ IsIntegral.mem_minimalPrimes_map_under

You can run this locally as follows
## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.


No changes to strong technical debt.
No changes to weak technical debt.

@github-actions github-actions Bot removed the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label May 21, 2026
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