Geodesic
A Note on Semiprime Rings with Torsionless Injective Envelope
Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 429-431

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Satyanarayana establishes in [6] that a semiprime right selfinjective ring with ACC on annihilator right ideals is semisimple Artinian, thereby extending a similar result of Koh [5] for prime rings. A theorem of Faith [3, Theorem 5.2], shows that the annihilator chain condition on either side implies that a right selfinjective semiprime ring is semisimple Artinian. Noting that any selfinjective ring has torsionless injective envelope we consider the possibility of replacing selfinjectivity by torsionless together with an annihilator condition. 
Armendariz, Efraim P. A Note on Semiprime Rings with Torsionless Injective Envelope. Canadian mathematical bulletin, Tome 16 (1973) no. 3, pp. 429-431. doi: 10.4153/CMB-1973-067-7
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     title = {A {Note} on {Semiprime} {Rings} with {Torsionless} {Injective} {Envelope}},
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     year = {1973},
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     doi = {10.4153/CMB-1973-067-7},
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