A non-Chinese (laowai) can own one apartment in his / her name for residential purposes only.  Can not rent it out, must live in it,.  Besides the fact that he or she must have the financial means to purchase it (banks will not lend money if you do not have a steady job in China for at least one year), the foreigner must have resided in China for at least one year at the time of purchase.

This is to avoid people to try to buy apartments as an investment to make money if they are not Chinese born.

of course, another way is to form a wholy foreign own corporation, and they buy whatever you want in its name.