Is my prayer at home immediately after the Dhuhr adhan on Friday valid, or must I wait until the men return from the Friday prayer?

It is permissible for someone who is not obligated to attend Friday prayer to pray Dhuhr once they are certain its time has entered, whether that is before men pray Jumu'ah or during it, while noting that some countries may call the adhan for Jumu'ah before the time for Dhuhr.