Geodesic
On Prime Rings with Ascending Chain Condition on Annihilator Right Ideals and Nonzero Infective Right Ideals
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 443-444

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If I is a right ideal of a ring R, I is said to be an annihilator right ideal provided that there is a subset S in R such that I is said to be injective if it is injective as a submodule of the right regular R-module RR . The purpose of this note is to prove that a prime ring R (not necessarily with 1) which satisfies the ascending chain condition on annihilator right ideals is a simple ring with descending chain condition on one sided ideals if R contains a nonzero right ideal which is injective. 
Koh, Kwangil; Mewborn, A. C. On Prime Rings with Ascending Chain Condition on Annihilator Right Ideals and Nonzero Infective Right Ideals. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 443-444. doi: 10.4153/CMB-1971-078-X
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