Abstract
For a ring A, the following assertions hold. (1) If A is a right p-injective ring with the maximum condition on right annihilators, then A is semiprimary. (2) If A is a right self-injective ring, then l(A1 ⋂A2) = lA1) + l(A2) for any right ideals A1 A2 of A. (3) If A is a right self-injective ring, then l(r(B)) = B for any finitely generated left ideal B of A. (4) If A is a right self-injective ring with the maximum condition on left annihilators, then A is a left Artinian ring with the maximum condition on right annihilators.
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