In terms of ZED travel American Eagle is just deemed as the commuter part of American and so the tickets are valid on both provided that American Eagle is the operating carrier rather than the marketing carrier where the flight is physically operated by another carrier in which case your ticket must be valid for that carrier.
Note: Other carriers on the same route should take your ZED ticket but some don't really know the rules so to guarantee acceptance get the ticket endorsed as valid for all such carriers.

P.S. I'm assuming you mean DFW and not DWF !!