Section 2.3-3.1 Due May 4

1. I didn't understand what the integral domain ring was. I was also confused by the definition of a field, because I'm used to my linear algebra teacher's definition. But maybe these two aren't the same thing. Also the example on page 43 of the set T= (r,s,t,z) was so much different then the other examples, and the addition and multiplication in the tables was defined strangely.
2. It's interesting how much these rings remind me of vector spaces. The definition is almost the same if not the same, as well as the properties. Also, a subring seems just like a subspace. Are these simply two names for the same concept?