In the Mai-Otome universe, a GEM (hypocorisitic for Generable Enigmatic Matrix) is the means by which an Otome is able to access her powers.

GEMs come in pairs, one of which is worn by the Otome in her left ear, whilst the other is usually kept on a ring worn by her Master (the exceptions being the Five Columns and Garderobe's staff and students, whose master is the Founder and Mai Tokiha and her Master Nekogami-sama, who has ingested the ring inadvertantly).

In order for a Meister (barring Columns and staff) to materialise her robe and Element, she must first seek certification from her Master, which is usually achieved by the Master kissing the GEM on the ear. However, as proven by the case of Nekogami and Mai, this is more ceremony than actuality.