I'm pretty sure it's a 0.1 ohm in a 2 watt or 3 watt package.
The main reason they blow is because your main semiconductor (triac?) has probably crapped itself, but you might be lucky and it's just the resistor.
So how do you know the resistor is blown? They dont normally show any external symptoms.
If that is a .1 ohm resistor then your meter will show it as a short, that may not be the problem.
There is probably a semiconductor, probably a triac. And it's probably blown. And you should probably take it to a qualified repairer of mains appliances since you have trouble even finding the triac (please don't be offended).