fractional ideals If $D$ is a domain and $K$ is field then for $x\in K$, $xD$ is a fractional ideal of $D$. If $xD$ and $yD$ are two fractional ideals, then is it true or not that $xyD\subseteq xD$ ? Thanks.

Dylan's example pretty much wraps up the question, but we can come up with another point of view: suppose 
$$xyD\subset xD\Longrightarrow \forall d\in D\,\,\exists\,d'\in D\,\,\,s.t.\,\,\,xyd=xd'\Longrightarrow x(yd-d')=0\Longrightarrow$$
$$\Longrightarrow x=0\,\,\,or\,\,\,yd=d'$$as we're in a domain or in its fractions field. 
If $\,x=0\,$ the claim is trivially true (as $\,0\cdot yD=\{0\}\subset 0\cdot D\,$), otherwise 
$$\forall d\in D\,\,\,\exists\,d'\in D\,\,\,s.t.\,\,\,\,yd=d'$$and taking $\,d=1\in D\,$ we get that $\,y\in D\,$, which of course could be not the case.
