Fortunately I have not broken my arm. People that I know who have broken their arm say their biggest complaint is that they can't wash their good hand. So being the problem solver that I am, I found this little foot shaped foot scrubber at Wal-Mart. It has suction cups on the bottom and very soft rubbery little strips attached to the top.
So we gave it a try to wash to wash one hand, and it works very well. Just dampen it, and a little squirt on soft soap or foaming soap then briskly rub your hand top and palm back to front. Run a little water to rinse it off and just leave it in the sink. It's not hard to dry one hand, but it is sure hard to wash it.