Hungerford says that we haven’t yet discussed subtraction with rings and he points out that . Yet I can’t see how this is different from what we are already have done. The first and second parts of that equation are equivalent but they are different given that the first deals explicitly with subtraction and the second addition with a negative value. I guess that the main difference is that now he explicitly mentions that this is how subtraction is defined: the addition of a negative value.
I wonder what the difference is between a finite integral domain and an ‘infinite’ integral domain.