feat(RingTheory/NoetherNormalization):Add noether normalization lemma

[su00000]

This PR contains a proof of Noether normalization lemma: Let A be a finitely generated algebra over a field k. Then there exists natural number $r$ and an injective homomorphism from k[X_1, X_2, ..., X_r] to A such that A is integral over k[X_1, X_2, ..., X_r].

Co-authored-by: Riccardo Brasca [email protected] Co-authored-by: Wan Lin [email protected] Co-authored-by: Xiaoyang Su [email protected]

• [ ] depends on: #18244

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[github-actions[bot]]

PR summary 613e535399

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.NoetherNormalization (new file)	1403

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Declarations diff

+ Quotient.mk_bijective_iff_eq_bot + T1 + algebraMap_finiteType_iff_algebra_finiteType + exists_finite_inj_algHom_of_fg + exists_integral_inj_algHom_of_fg + exists_integral_inj_algHom_of_quotient + map_coe + ofDigits_inj_of_len_eq

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#18244~~ By Dependent Issues (🤖). Happy coding!

[riccardobrasca]

Can you please fix the conflict? Thanks!

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by riccardobrasca.

[riccardobrasca]

Sorry, one last thing: can you add a TODO saying that we can take s in the final theorems equal to the Krull dimension of R?

[su00000]

Sorry, one last thing: can you add a TODO saying that we can take s in the final theorems equal to the Krull dimension of R?

Sure

[mathlib-bors[bot]]

:v: su00000 can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[su00000]

bors r+

[mathlib-bors[bot]]

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[riccardobrasca]

Two hours without merging master and there is of course an error... it's probably a lemma about quotient that had implicitness of some variable changed. Feel free to fix and merge.

[riccardobrasca]

I pushed a fix to Operations.lean but it will surely break something in the final file.

[su00000]

bors r+

[mathlib-bors[bot]]

Pull request successfully merged into master.

Build succeeded:

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