No ticket needed if you choose not to buy the infant a seat; just add the infant at check-in. There's no linkage between the INF and the adult from a fare standpoint, i.e. how the adult got his seat. AA does not add infants in the adult reservation or create one for the infant; the whole thing it's handled at check-in only.

Carrying a lap infant in the US is much less bureaucratic that with non-US airlines/itineraries, as AA and its brethren have not discovered that infants could be yet another source of fee income.

Read http://www.flyerguide.com/wiki/index...and_Fares_(AA)