separable

Separable extensions

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Equivalent characterizations: attachments/Pasted%20image%2020220123204633.png

Over perfect fields: attachments/Pasted%20image%2020220123204738.png # Separable algebras

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attachments/Pasted%20image%2020220123204522.png # Results

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trace map

Relation to separable algebras:
absolute Galois group

Warning: \(\mkern 1.5mu\overline{\mkern-1.5muk\mkern-1.5mu}\mkern 1.5mu/k\) may not be Galois! Hence the need for a separable closure.