Does divorce occur if a man divorces his wife in private?

If a man divorces his wife verbally and hears himself, the divorce takes effect whether the wife is present or absent, and whether others are present or not. His claim of jest or playfulness does not benefit him. However, if he speaks to himself about divorce or intends it in his heart without uttering it, it does not take effect. If he writes a divorce but does not intend divorce by it, it does not take effect; but if he intends it by writing, it does take effect.