feat(RingTheory/KrullAkizuki): add the Krull-Akizuki theorem

[Yangdx02]

This PR proves the Krull–Akizuki theorem. It proves that if $A$ is a one-dimensional Noetherian domain with fraction field $K$, $L / K$ is a finite extension, and $B$ is a subring of $L$ containing $A$, then $B$ is a Noetherian ring of Krull dimension at most one, and every nonzero ideal of $B$ has finite $A$-length quotient.

Main results:

• krullAkizuki_isNoetherianRing
• krullAkizuki_dimensionLEOne
• krullAkizuki_quotient_ideal_finiteLength
• krull_akizuki

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[github-actions]

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[github-actions]

PR summary 99f270af37

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.KrullAkizuki (new file)	1878

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Declarations diff (regex)

+ Submodule.exists_smul_mem_of_fg
+ build_fg_witness
+ exists_free_submodule_of_rank
+ finiteLength_quotient_of_fg
+ ideal_inter_of_aeval_eq_zero
+ krullAkizuki_B_rank_le
+ krullAkizuki_dimensionLEOne
+ krullAkizuki_ideal_inter_nonzero
+ krullAkizuki_isNoetherianRing
+ krullAkizuki_quotient_ideal_finiteLength
+ krull_akizuki
+ length_fg_quotient_eq_bound
+ length_free_quotient_smul
+ length_ker_eq_length_coker
+ length_ker_smul_eq
+ length_quotient_chain
+ length_quotient_smul_eq_free
+ length_quotient_smul_le
+ quotient_isArtinian_of_nonzero
+ range_smul_mkQ

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.

Declarations diff (Lean -- pending)

Computed after the build finishes.

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
5011	1	exposed public sections

Current commit 99f270af37
Reference commit f98b1aa39a

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).