I have moved into an apartment where the kitchen sink was put in as an afterthought and as such was not vented in any way. Is there a way to simply tee off from the drain and run a short stretch of PVC under the basin of the sink and up to above the level of the drain in order to vent the drain?
I have seen reference to what someone calls a cheater vent, any idea what that is and how to make one?
Thank you in advance for any help I receive. :o

You're referring to a mechanical vent, and yes, you can cut in a tee in the line after the trap and install one. To check them out click on,
http://www.studor.com/homeowners.htm
Since this is a one way vent you don't have to extend it up over the flood rim of the sink. Just mount it on the branch of a upright tee .
Good luck, Tom