refactor(FieldTheory): split Mathlib.FieldTheory.Purelyinseparable

[mistarro]

---

[github-actions]

PR summary b83de8e32a

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.FieldTheory.PurelyInseparable	1534	0	-1534 (-100.00%)
Mathlib.FieldTheory.CardinalEmb	1537	1535	-2 (-0.13%)
Mathlib.FieldTheory.JacobsonNoether	1560	1558	-2 (-0.13%)
Mathlib.RingTheory.Unramified.Field	1951	1949	-2 (-0.10%)
Mathlib.FieldTheory.IsPerfectClosure	1536	1535	-1 (-0.07%)

Import changes for all files

Files	Import difference
Mathlib.FieldTheory.PurelyInseparable	-1534
4 files Mathlib.FieldTheory.CardinalEmb Mathlib.FieldTheory.JacobsonNoether Mathlib.RingTheory.Etale.Field Mathlib.RingTheory.Unramified.Field	-2
Mathlib.FieldTheory.IsPerfectClosure	-1
Mathlib.FieldTheory.PurelyInseparable.Basic (new file)	1532
Mathlib.FieldTheory.PurelyInseparable.RelPerfectClosure (new file)	1535
Mathlib.FieldTheory.PurelyInseparable.Tower (new file)	1536

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

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).

[acmepjz]

Thank you very much! Looks good to me. I haven't spot any mistakes.