She signed a document renouncing her inheritance rights.

renouncing 是动词 renounce 的现在分词形式。renounce 由前缀 re-（表示"反向、反对"）和词根 nounce（来自拉丁语 nuntiare，意为"宣布"）组成，字面意思是"宣布反对"，引申为"正式声明放弃（权利、头衔等）"。