Empress Radhanan was the ruler of the Seanchan Empire, although her name is not used outside the imperial family. She was murdered by Semirhage along with all the imperial family left in Seanchan (KoD, Prologue). It was she who authorized Tuon to be trained as sul'dam and who appointed Anath as her soe'feia. She named Tuon as her heir before she died.
During the last thousand years, the Seanchan Empire has always been ruled by a woman of the blood of Luthair Paendrag Mondwin, the son of Artur Hawkwing (WH, Ch. 14), the last emperor was Algwyn (WH, Ch. 14). It seems unlikely that this is a formal arrangement as in Andor, as Turak said he was twelfth in line to the throne (TGH, Ch. 34).
Empress Radhanan married a man she loved, who, according to Tuon, died of a bad wager (CoT, Ch. 28).