but the chances are that a green ring would simply mean menthol, I can't think of any brand I've seen/smoked that has a green on them at all other than menthols
Menthol cigarettes tend to have a totally white tip also, so if it was all white with just a green ring they will be menthol. Most menthol in different brands are green packaging also, so if you know its not green, they may be easier to find.