Re: semisimple rings

[Jannick Asmus]

On 30.10.2006 22:46, Thunder wrote:
> Show that  Q[x,y]/(x^2,xy) is not semisimple.
> The teacher wrote that it is because [x^2]=0
> why is that? 

Perhaps he meant [x]^2=0 (where [x] is not zero)?

If so this is correct since (ii) of the following characterization is
not fulfilled. A ring is semisimple iff (i) it is artinian and (ii) its
radical is zero.