3.2, due January 24

All this talk about rings reminds me of a song: "If you liked it then you shoulda put a ring on it..." Ok now that that is out of my system, let's get back to Abstract Algebra.  This section seemed to follow quite nicley with the things we talked about in class on. The one thing that was not the easiest to understand was Theorem 3.6.  I thought that for S to be a subring of the ring R, it had to satisfy addition and multiplication under R( at least that's the way I understood what Dr. Forcade said), but in Theorem 3.6, S has to be closed under subtraction and mulitplication in S.  The rest of the section follows from simple logic.  Well I guess it's more intuition but you have to prove it first before you can actually use it.  As I read the example of (a+b)^2, I instinctively thought a^2 + 2ab + b^2, but as I read I remembered that R is not necessarily a commutative ring. That'll be a tough one to remember.