3.1 part 2, due on September 14

1. The most difficult part was probably keeping the three plus signs straight in the Cartesian product example.  The example itself wasn't that difficult, though; it makes sense that the Cartesian product of two rings is itself a ring.

2. The conditions required for a subring reminded me of the conditions required to show that a subset of a vector space is a subspace (from Math 313 and my ACME classes).  In both cases, a harder problem becomes easier when it's inside something that already satisfies the conditions.