feat(Algebra/TrivSqZeroExt): the canonical ideal has square zero

[AntoineChambert-Loir]

• Define TrivSqZeroExt.kerIdeal: the canonical ideal of TrivSqZeroExt R M
• Prove TrivSqZero.sqZero: this ideal has square zero.

co-authored with @mariainesdff

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[github-actions]

PR summary 4166dc3b98

Import changes exceeding 2%

%	File
+11.18%	Mathlib.Algebra.TrivSqZeroExt

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.TrivSqZeroExt	1002	1114	+112 (+11.18%)

Import changes for all files

Files	Import difference
Mathlib.Topology.Instances.TrivSqZeroExt	46
Mathlib.LinearAlgebra.TensorAlgebra.Grading	82
Mathlib.LinearAlgebra.FreeProduct.Basic Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower	83
Mathlib.LinearAlgebra.SymmetricAlgebra.Basic Mathlib.LinearAlgebra.TensorAlgebra.Basic	90
Mathlib.Data.Matrix.DualNumber	99
Mathlib.Algebra.DualNumber Mathlib.Algebra.TrivSqZeroExt	112

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Declarations diff

+ kerIdeal
+ mem_kerIdeal_iff_exists
+ mem_kerIdeal_iff_inr
+ sqZero

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 scripts/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).