When to omit the modifying 的？ 他给她买来了一个戒指。
He gives her a ring that he bought.


I assume that this sentence should need 的 before "a ring that he bought" to be modifying, as below.

他给她买来了'的'一个戒指。


So I think 的 is somewhat omitted.

I'd like to know what rule can be generalized from this case.

Thanks in advance, and also Happy new year!
他给了她一个他买的戒指 (he gives her a ring that he bought) seems grammatical，but may sound strange， maybe one could also say 他作为礼物买了一个戒指给她 （he bought a ring for her as a present）

for the following cf。外国人实用汉语语法：

in the attributive， verb＋的， 的 generally can not be omitted，

examples：讨论的问题，旅行的人都来了，请的客人都到了

exceptions exist with 的 optional ；我看见过游行队伍 （some dissyllables modifying dissyllables）