Abstract
A right ideal A of a ring R is called annihilator-small if A+T=R, T a right ideal, implies that [Formula: see text], where [Formula: see text] indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it is annihilator-small are given, its relationship to the total of the ring is examined, and its connection with related rings is investigated.
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