What Are the Embeddings of K in C?

In summary, K has six embeddings in C. The only embedding for Q is the identity, where 1 goes to 1, meaning that N also goes to N and Q goes to Q. The other five embeddings depend on the choices made for i and its cubic root. It is necessary to find an element that squares to 1 and 1 must go to 1. The process of formalizing these choices may lead to a better understanding of K's embeddings.
  • #1
Palindrom
263
0
Let K=Q(i,(1+i)^(1/3)).
Describe all of K's embeddings in C.
(C-Complex Field, Q-Rational Field).

Describe? Could it be the answer is just the identity? How could I prove that?

Thanks in advance! :smile:
 
Physics news on Phys.org
  • #2
i must go to some element that squares to 1, and 1 must go to 1, so how many choices can that be?
 
  • #3
Good point, stupid me.
(You meant -1 I suppose).

So actually, it is true that for Q, the only embedding is id?
(1 must go to 1, therefore N - Natural numbers - must go to N, and therefore Q must go to Q)

And in this case, I have like... 6 choices or so? (i goes to i or -i, plus playing with the cubic root a little bit)

I'm going to go try and formalize it. I'll come back if I have any prob.
Thanks a lot!

Oh, and if I wrote sth. stupid, feel free to throw it in my face. :biggrin:
 

FAQ: What Are the Embeddings of K in C?

What is the "Fields- strange problem"?

The "Fields- strange problem" is a theoretical physics problem that deals with the concept of fields, which are regions of space that have certain properties such as energy or force. The problem is centered around the strange behavior of particles within these fields, and how they interact with each other.

Why is the "Fields- strange problem" important?

This problem is important because it challenges our current understanding of physics and the fundamental forces that govern the universe. It also has potential implications for future technologies and our understanding of the nature of reality.

How is the "Fields- strange problem" being studied?

Scientists are studying this problem through a combination of theoretical models and experiments. They use advanced mathematical equations and computer simulations to analyze the behavior of particles in different field configurations.

What are some potential solutions to the "Fields- strange problem"?

There are various theories and proposals that attempt to explain the strange behavior observed in fields. Some suggest the existence of new particles or forces, while others propose modifications to existing theories such as quantum mechanics or general relativity.

How might the "Fields- strange problem" impact our understanding of the universe?

If a solution to this problem is found, it could significantly change our understanding of the universe and its fundamental laws. It may also lead to new technologies and advancements in areas such as energy production and quantum computing.

Similar threads

I Is the Order of an Automorphism in a Field with Characteristic p Equal to p?
Replies
2
Views
1K
I Finite fields, irreducible polynomial and minimal polynomial theorem
Replies
6
Views
2K
MHB Smallest subfield of C that contains i
Replies
4
Views
2K
I Proving inequality about dimension of quotient vector spaces
Replies
0
Views
690
I Show that ##\mathbb{C}## can be obtained as 2 × 2 matrices
Replies
14
Views
2K
MHB Statements with linearly independent vectors
Replies
10
Views
1K
MHB Show that Q[π] is not a subset of Q(π)
Replies
8
Views
2K
I On a bound on the norm of a matrix with a simple pole
Replies
8
Views
2K
MHB Discrete valuation Ring which is a subring of a field K Problem
Replies
3
Views
2K
I Need clarification on a theorem about field extensions/isomorphisms
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top