Section 3.1-3.2 Due May 6

1. For some reason I'm still confused about what an integral domain is, and how if it is finite, it is a field. In theorem 3.6 it says that a subset of a ring is a subring if it is closed under subtraction and multiplication, but before it was addition and multiplication. Does it have to be all three or just either subtraction or addition?
2. The properties seem pretty usual. The exponent rules are the same as for the reals, as well as squaring a+b. None of the properties of rings seem out of the ordinary. The fact that there are many units in the matrix ring M(Z) is interesting.