Let S be a ring = RxR (real#,real#). Find all the ideals in RxR.
We were told that there are only 4.
The Attempt at a Solution
I can only think of these 4 sub-rings of S, (R,0), (0,R), (R,R) and (0,0). And each seem to be ideal. Are these the correct 4? What other sub-rings of RxR are there but not ideal?