冷気の指輪 [reiki no yubiwa] or 'frost ring' in Japanese.
Final Fantasy XIII-2
Frost Ring
Slot cost: 55
Ability: Resist Ice +33%, Accessory Ability Group: Fire Damage
Buy: 1,000 gil (sell: 500 gil)
Treasure: Sunleth Waterscape (300 AF)
Description: ?
Delicate Frost Ring
Slot cost: 50
Ability: Resist Ice +29%, Accessory Ability Group: Fire Damage
Buy: 1,500 gil, Frost Ring, Cie'th Tear x2 (sell: 750 gil)
Description: ?
Durable Frost Ring
Slot cost: 60
Ability: Resist Ice +39%, Accessory Ability Group: Fire Damage
Buy: 500 gil, Frost Ring, Enigmatic Fluid x2 (sell: 250 gil)
Description: ?
Pictlogica

Stats (lv1): strengthens Ice-element attacks
Buy: - (sell: ? gil)
Obtain: Condor Wildlands, event quests Challenge the Magic Castle, First Frost of Harvest Moon and Fortress of Ice Fog
Use: EX Alchemy for Spirit Armlet upgrades
Type: Accessory, Rarity: ★★★, Element: -
Category: Equipment