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“For Isildur would not surrender it to Elrond and Círdan who stood by. They counseled him to cast it into the fire of Orodruin night at hand... But Isildur refused this counsel, saying: 'This I will have as weregild for my father's death, and my brother's. Was it not I that dealt the Enemy his death-blow?' And the Ring that he held seemed to him exceedingly fair to look on; and he would not suffer it to be destroyed.” - The Silmarillion
Or are you referring to another ring?