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## Homework Statement

Let S be a ring = RxR (real#,real#). Find all the ideals in RxR.

## Homework Equations

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?