If your professor has already solved the problem, perhaps it would be better for you to comment what particular doubts have you had.
Fernando Revilla
I'm working with elementary rings, and my professor gave me about ten of these to start but it seems like a lot of work with how he managed it. I know you guys don't answer homework so I chose one my professor solved to help me compare so I can do the others. Any help would be greatly appreciated, the groups were easy but the rings are a little more difficult for me to grasp.
Consider the set R = {a + b (SQRT 2): a, b are in Z}
Prove that R is a subring of R.
Is R commutative?
Does R have identity?
Is R an integral domain?
Is R a division ring?
Is R a skew field?
Is R a field?
If your professor has already solved the problem, perhaps it would be better for you to comment what particular doubts have you had.
Fernando Revilla