Will this kitchen sink drain piping work in my 1920 house? See pix/diagram (pdf)

Hi, I've already built this, but before I seal it up (!!!) , will this kitchen drain piping work? Specifically is the horizontal (it is level) section problematic? Is no venting a problem? Detail: I have a house built in 1920 with a cast iron kitchen drain whose horizontal section leaked into my basement. Black mold, etc... So I busted the old tiled concrete wall, http://www.netdevi.com/kitchen drain plumbing.pdftook out the old piping and replaced it with PVC. There is a dishwasher also connected. See picture / diagram. Would much appreciate feedback/direction.