After breaking up, is it considered ethical to greet your ex on his/her birthday? Even if you still have grudges in him/her?

You might think that with greeting your ex, you are giving him an impression that you still like him/her and wants him/her back. With that in mind, you want to avoid that connotion thus thinking that it’s better not to greet. But will your ex think that it seemed you don’t care at all? Thinking that it seemed like you two didn’t have any history at all?

Hmm…just a thought.