If A is an additive subgroup of a ring R, A is said to be an ideal if Ra is contained in A for all a in A; that is, if every multiple of an element of A is again in A. Is it true that A is an ideal of R if Ar is contained in A for all r in R? To me it seems like they are equivalent statements but I'm not sure. Update: Second thought, I believe these are NOT equivalent statements. I'm looking at the proof that explains why if 1 is in A then A = R, and you could not employ this argument under the faulty definition I tried to push. Anyone wanna shed further light on the difference between these statements?