6.3, due Feb 22

1. Ok, the most difficult part of this section for me was the theorems about something being maximal. I understand the definition of maximal, but then I just think I'm getting a little confused with the theorems. Like Thm 6.15, so I understand that if M is an ideal in a comm. ring R with identity, then M is maximal if R/M is a field. So going on to corollary 6.16, in a comm ring R with identity, evey maximal ideal is prime. So does that mean that whenever R/M is a field (along with the other condition) that M is always a maximal ideal, and it's prime?
2. I like that I've seen things in this section before, such as the definition of prime on p154, that is the same as the one we had in chapter 2 I think, so that's nice. It has been a pretty interesting section too, inda fun to read about.