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Late reply, but in case you're still wondering... The tattoo is the 'knowledge' on how to create fire alchemy. It is the product of her father's research and the key to becoming a fire alchemist like Mustang. That's why after the Ishval war, Riza asked Mustang to burn her tattoo, so that no one can access that knowledge again and become another fire alchemist and cause destruction (well, that's according to the anime, I'm about to start the manga now) (=・ω・=)
Wait, can anyone tell me the meaning behind the tattoos on Riza's back? I'm still lost at that part