On 08/05/2012 06:23 PM, Warp wrote:
> Invisible<voi### [at] devnull>  wrote:
>> No. Quaternions do not form a field. Neither do the hypercomplex
>> numbers, nor any of the other 4D generalisations.
>
>    The reason is that it's not possible to make multiplication commutative
> for them.

The hypercomplex numbers possess commutative multiplication. What they 
do /not/ possess is multiplicative inverses. (Not for all elements, anyway.)

In short, you can construct lots of 4D number systems, all of which fail 
to be a field in a different way.

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