I screwed on a new shower hose on to my shower arm. I used an adjustable wrench to make it tight. I screwed it too hard and the thing broke (it was non metal, probably plastic). Now there is a broken off piece still remaining on the threads of the shower arm! I have tried and tried to remove it myself (by hand). I tried the wrench and it does not budge. I cannot mount a new piece until the broken piece comes off. Please tell me what kind of tool I needs to take this piece off...thanks for your help.
I should add the "nut" (for lack of a better word) is smooth and has no ridges so a wrench type tool will not grasp and turn it.

You can try to heat the plastic nut and melt & remove.

otherwise try cutting spaner....