Let be the quaternion algebra.

Show that is a division algebra, i.e.

if xy = 0, then x = 0 or y = 0.

I understand this but I am not sure how to prove it. Is it as simple as just multiplying by x and y inverse?

and

????

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- Aug 27th 2011, 06:48 PMdwsmithquaternion algebra
Let be the quaternion algebra.

Show that is a division algebra, i.e.

if xy = 0, then x = 0 or y = 0.

I understand this but I am not sure how to prove it. Is it as simple as just multiplying by x and y inverse?

and

???? - Aug 27th 2011, 08:29 PMFernandoRevillaRe: quaternion algebra
Essentially you are right. Suppose and . We have to prove or . If then

Similar reasoning if we suppose . - Aug 27th 2011, 09:13 PMdwsmithRe: quaternion algebra

How do I go about showing that is a basis of - Aug 27th 2011, 11:36 PMFernandoRevillaRe: quaternion algebra
implies . Now use that is a division algebra.

- Aug 29th 2011, 11:02 AMDrexel28Re: quaternion algebra