Suppose R and S are rings, and consider the following subsets of RXS:
R'={(r,0s) such that r belongs to R} and S'={(Or,s) such that s belongs to S} where 0s is the zero element of S and 0r is the zero element of r.
1) If R=Z3 and S=Z5, what are the sets R' and S'?
I'm not sure, is it, R'={(r,5k) for k an integer, and r belongs to R} and S'={(3k, s) for k an integer, and s belongs to S}?
2) Prove that for any rings R,S, we have the R' is a subring of RxS and S' is a subring of RxS. I think I would just need to show the four things, which I could probably do, but I want to make sure my part 1) is correct first.
Thanks.
CANCEL---I SOLVED IT