Is it permissible to publish academic achievement certificates on Facebook, and is that considered showing off?

Publishing one's certificate on Facebook is not considered showing off (riya'); for riya' is performing an act of obedience while mindful of other than God. There is no impediment to doing so if it is not intended for boasting, especially if there is a need for it, such as announcing one's educational level. It is better to avoid it if there is no need, and it becomes forbidden if it is intended for boasting, showing off, and self-aggrandizement, because it is a degree of arrogance (kibr).