feat(RingTheory/Localization/Pi): localization of a finite direct product where each semiring in product has maximal nilradical is a projection

[maddycrim]

For noncomputable def urjectivePiNilradicalIsMaximal : Let M be a submonoid of a direct product of commutative rings R i.
If each R i has maximal nilradical then the direct product ∏ R i surjects onto the
localization of ∏ R i at M.

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[github-actions]

PR summary 5b97412114

Import changes exceeding 2%

%	File
+32.80%	Mathlib.RingTheory.Localization.Pi

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Localization.Pi	872	1158	+286 (+32.80%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.Localization.Pi	286

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Declarations diff

+ algebraMap_pi_surjective_of_nilradical_isMaximal
+ surjective_piRingHom_algebraMap_comp_piEvalRingHom_of_nilradical_isMaximal

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.

---

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).

[Paul-Lez]

(untested)

Suggested change

	refine ⟨r, Bijective.injective (bijective_lift_piRingHom_algebraMap_comp_piEvalRingHom R S _ M)
	?_⟩
	refine ⟨r, (bijective_lift_piRingHom_algebraMap_comp_piEvalRingHom R S _ M).injective ?_⟩

[Paul-Lez]

Suggested change

	[IsLocalization M S'] [Fintype ι] : Surjective (algebraMap (Π i, R i) (S')) := by
	[IsLocalization M S'] [Fintype ι] : Surjective (algebraMap (Π i, R i) S') := by