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

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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. Participants clarify that in the context of the proposition, the symbol $$F$$ is indeed a typographical error and should be replaced with $$K$$. This correction is crucial for accurately understanding the homomorphism $$U(F) \rightarrow U(F)$$ as it pertains to Galois Theory and field extensions.

PREREQUISITES
  • Understanding of Galois Theory concepts, particularly field extensions.
  • Familiarity with homomorphisms in abstract algebra.
  • Knowledge of the group of units in ring theory.
  • Experience with reading mathematical propositions and proofs.
NEXT STEPS
  • Study the implications of automorphisms in field extensions within Galois Theory.
  • Review the group of units in ring theory and its applications.
  • Examine other propositions in Chapter 8 of Lovett's book for deeper insights.
  • Explore additional resources on homomorphisms and their properties in abstract algebra.
USEFUL FOR

Students and educators in mathematics, particularly those focusing on abstract algebra and Galois Theory, will benefit from this discussion. It is also valuable for anyone seeking to clarify typographical errors in mathematical texts.

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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 ...
 
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You are correct, $F$ should be $K$.
 
Euge said:
You are correct, $F$ should be $K$.
Thanks Euge ...

Peter
 

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