The Argon ring is a special accessory in Dragon Quest VIII.
An Argon Ring was once possessed by Former Argonian Prince, Eltrio. He later presented it as a gift towards his love, Xia, a Dragovian woman. She later kept the ring as a reminder of him after he died attempting to reach the Dragovian Sanctuary to meet with her again.
Years later, their son, The Hero defeated the Lord of the Dragovians in battle and was met with gratitude. The Hero was instructed by the Dragovian Lord to speak with Chen Mui in regards to learning about his own past. Upon doing so, he was presented with the Argon ring that was kept by his mother.
Six months after the defeat of Rhapthorne, the wedding of Princess Medea of Trodain and Prince Charmles of Argonia was about to occur. Though The Hero & his party escorted Medea, they were denied an attendance by Charmles dismissing them as commoners. Angelo, angered by that statement and the fact that he's marrying the princess remembered the Argon ring that The Hero had and suggested that he shows it to King Clavius in hopes of preventing the marriage.
The Hero showed Clavius the ring as suggested. Despite some hesitation on his part, Clavius decided that with the ring as evidence, he was the rightful groom.