3.2, Due on January 24

Difficult:
I had a hard time understanding the definition of a unit. I got confused because I sounded to me like every ring with identity may not always have a unity, but I thought that was the definition of being a ring with identity. If a ring has identity, then it has a multiplicative inverse. But the definition made it sound like a ring with identity only has a unit if there exists and element a such that ua=1=au. I just was confused if there is a unit for every ring with identity.

Connection:
I really liked this section. I like that subtraction in a ring is defined as most people think of subtraction (just adding a negative). I like that arithmetic in rings, for the most part, is something that I am familiar with. For example, theorem 3.5 made a lot of sense to me. I like when I am able to follow the logic of the proofs and understand the meaning of the theorems.