I am in the middle of finishing my basement and want to add a sink that will attach to an existing kitchen drain from above. I don't have a way to vent the sink easily unless I use a Air Admittance Valve. The drain will run about 5 feet, make a 90 degree and run another 4 feet. Would the attached diagram work correctly? Anything in blue is the new plumbing.
The valve needs to be downstream of the trap, basically in the position an actual vent would be.
Also, be sure they're legal where you are. My local inspector forced me to run a new vent line and tie into the existing stack above the upstairs sink drain when I wanted to add a laundry drain.