bonus question on quaternions

Asked Mar 07 '13 at 19:17

Active Mar 07 '13 at 19:17

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I have this asterisk question, I know its hard to do and I know no one would get it in my class. Just wondering if any of you guys could give me good hints in how to do this. It would be appreciated.

Thank you

Question

The quaternions extend the complex numbers and give non-commutative products on points of $\mathbb{R^4}$. They satisfy every field axiom except for the commutativity of multipication. Show that there is no commutative product making $\mathbb{R^n}$ a field for $n \geq 3$. For $n=2$ the field is the complex numbers.

asked Mar 07 '13 at 19:17

MathGeek

A proof can be found on the wiki page of Frobenius theorem for real division algebras. (I've problem to include the link directly). – achille hui Mar 07 '13 at 19:23
Remember this person who is also in your class? It seems they already found a proof and asked about it. – Mar 07 '13 at 19:28
1

They should really hang out together more ... – Hagen von Eitzen Mar 07 '13 at 19:28
who are these guys, i am going to go find these people. but they are in new zealand when im like 100 000 miles away from them lol – MathGeek Mar 07 '13 at 21:48

bonus question on quaternions

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