My attempt: let $f$ ($w$+$x$i+$y$j+$z$k) $=$ ($w$+$x$i,$y$+$z$i)
then I tried proving it is a homomorphism. $f$ is a homomorphism under addition but fails to be a homomorphism under multiplication.
Can anyone give any hint? Or any property I need to show they don't share.
Any help would be appreciated.