- #1

- 10

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Obviously, n=1 is a field, and n=2 can be made into a field (which is just the complex plane.)

So what about n>2?

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- Thread starter dreamtheater
- Start date

- #1

- 10

- 0

Obviously, n=1 is a field, and n=2 can be made into a field (which is just the complex plane.)

So what about n>2?

- #2

- 305

- 3

Even for R^2, your complex numbers, that's a space that's isomorphic with R^2, and is not R^2 itself. You can introduce invertable vector product for R^n (I like the geometric/clifford algebra product for this). But to get invertable and closed with that product you have to combine components of such vector products (ie: complex numbers, and quaternions, or other generalizations of these get by adding grade 0 and 2 components from this larger algebraic space).

- #3

- 176

- 0

I saw a proof of the fact in a complex analysis class sometime ago so I don't remember it but it uses (very) elementary methods and as such should be found easily.

- #4

matt grime

Science Advisor

Homework Helper

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- 4

I think that it might be better to say - if F is a field, and F is in VECT(R) - cat of real vector spaces - then F has dimension 1 or 2.

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