MHB Galois Theory - Fixed Subfield of K by H ....

[Math Amateur]

I am reading "Abstract Algebra: Structures and Applications" by Stephen Lovett ...

I am currently focused on Chapter 8: Galois Theory, Section 1: Automorphisms of Field Extensions ... ...

I need help with Proposition 11.1.11 on page 560 ... ...Proposition 11.1.11 reads as follows:
https://www.physicsforums.com/attachments/6664
In the above Proposition from Lovett we read the following:" ... ... Since $$\sigma$$ is a homomorphism $$U(F) \ \rightarrow \ U(F)$$ ... ... "My question is ... ... what is $$F$$ ... is it a typo ... does it mean $$K$$ ...Hoping someone can help ... ...

PeterNOTE: U(F) in Lovett means the group of units of the ring F ...

 

[Euge]

You are correct, $F$ should be $K$.

 

[Math Amateur]

You are correct, $F$ should be $K$.

Thanks Euge ...

Peter