Very long chains of annihilator ideals

Here we examine one of the two right Goldie conditions: the ascending chain condition on right annihilator ideals, r. ACC^⊥. One might well ask if a ring has r. ACC^⊥, does there exist a bound on the lengths of chains of right annihilator ideals? Under certain additional hypotheses, this bound does exist. In general, however, a bound does not exist, as is shown by the two example presented here.