Glowing stone - Scarab carving
Your description matches fluorite, you can see many pictures in Internet, and compare with your stone. To determine what it is precisely, you have to post a picture.

EDIT. After the pictures are posted, I take back my suggestion: the key difference 
is that fluorite is not transparent, at least those pieces that I possess, and those which I can see on Internet. But in the dark, it looks exactly of the right color. There  are very many fluorescent stones, look for example, here:
 http://www.galleries.com/minerals/property/fluotabl.htm