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

  • Thread starter Thread starter Math Amateur
  • Start date Start date
  • Tags Tags
    Theory
Click For Summary
The discussion centers on Proposition 11.1.11 from "Abstract Algebra: Structures and Applications" by Stephen Lovett, specifically regarding the notation used in the proposition. The user seeks clarification on whether the symbol F is a typo and should instead refer to K. Other participants confirm that F indeed should be replaced with K, as U(F) represents the group of units of the ring F. This correction is essential for understanding the context of the proposition in Galois Theory. The conversation highlights the importance of precise notation in mathematical texts.
Math Amateur
Gold Member
MHB
Messages
3,920
Reaction score
48
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 ...
 
Physics news on Phys.org
You are correct, $F$ should be $K$.
 
Euge said:
You are correct, $F$ should be $K$.
Thanks Euge ...

Peter
 

Similar threads

Undergrad Galois Theory - Fixed Subfield of K by H ....
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Galois Theory - Structure Within Aut(K/Q) ....
  • · Replies 6 ·
Replies
6
Views
3K
MHB Automorphisms of Field Extensions .... Lovett, Example 11.1.8 .... ....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Automorphisms of Field Extensions .... Lovett, Example 11.1.8
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Prime Subfiellds - Lovett, Proposition 7.1.3 ....
  • · Replies 4 ·
Replies
4
Views
2K
MHB Prime Subfiellds - Lovett, Proposition 7.1.3 ....
  • · Replies 5 ·
Replies
5
Views
2K
MHB Field Extensions - Remarks by Lovett - Page 326 .... ....
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Field Extensions - Remarks by Lovett - Page 326 .... ....
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Basic Notation for Field Extensions ....
  • · Replies 12 ·
Replies
12
Views
3K
MHB Basic Notation for Field Extensions .... ....
  • · Replies 2 ·
Replies
2
Views
2K