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What kind of gem is it?
A mild ammonia solution and a toothbrush usually works very nicely for even my costume jewelry. Don't leave it in the solution for long. Just half a minute max is usually enough. Too long and it'll eat away at some metals. Don't ask me which. Google "jewelry cleaning" and I'm sure you'll find many home mixes as well as commercial solutions. Vinigar works well too. Just use the toothbrush to clean in the grooves.
I usually take my rings off when I put lotion on because my wedding rings collect the creams in the grooves and get the backs of the stones dirty quickly. If my hands are too swollen to get my wedding bands off I'll put the cream on my palms and the back of my ringless hand and then rotate the wedding rings and put the lotion on the back of that hand while the stones are on the inside of that hand. It doesn't get as dirty as quickly that way.
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"Always learn the rules so that you can break them properly." Dalai Lama
My Karma just ran over your Dogma. 
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