Alex Rodriguez Says 'Onward and Upward' with Jennifer Lopez, Flies to DR

Things are looking up between Alex Rodriguez and Jennifer Lopez ... at least that's how A-Rod seems to view their relationship, now that they're in the same place.

TMZ has confirmed A-Rod flew to the Dominican Republic, where J Lo has been shooting a movie, and Monday morning he posted video from their luxury digs down there. His caption said, "Happy Monday. New week,. New day. Onward. Upward."

BTW, he also tagged J Lo tag in his post.

Remember, A-Rod told a photog Saturday in Miami he is definitely NOT single. He and Jennifer told TMZ, "We are working through some things."

Sources with direct knowledge told us those issues they're working on do not involve a third person.

Now, we're told A-Rod's been going to the DR every few weeks while Jen's been there shooting -- so this current trip could've been planned all along. Still, the fact he's carried through with it ... is a sign they might work it all out, after all.