---
date: 2022-01-15 21:49
modification date: Sunday 23rd January 2022 20:43:01
title: separable
aliases: ["separable", "separable extension", "inseparable", "separable degree", "separable closure"]

---

Tags: 
#NT/algebraic #AG 
Refs:
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# Separable extensions
![](attachments/Pasted%20image%2020220120134357.png)

Equivalent characterizations:
![](attachments/Pasted%20image%2020220123204633.png)

Over perfect fields:
![](attachments/Pasted%20image%2020220123204738.png)
# Separable algebras

![](attachments/Pasted%20image%2020210625203549.png)
![](attachments/Pasted%20image%2020220417010815.png)

# Separable degree
![](attachments/Pasted%20image%2020220123204522.png)
# Results

![](attachments/Pasted%20image%2020220123204318.png)
![](attachments/Pasted%20image%2020220123204841.png)


# Misc

![](attachments/Pasted%20image%2020220211124249.png)