Geodesic
A Note on a Prime Ring with a Maximal Annihilator Right Ideal
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 109-110

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A ring R is called a prime ring [1] if and only if a·R·b = 0 implies that a = 0 or b = 0 for all a, b ε R. Hence if R is a prime ring and a is a non-zero element of R, a·R ≠ 0 and R·a ≠ 0. In the present note we prove that a prime ring with a maximal annihilator right ideal has no non-zero nil right or left ideal. 
Koh, Kwangil. A Note on a Prime Ring with a Maximal Annihilator Right Ideal. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 109-110. doi: 10.4153/CMB-1965-014-x
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     title = {A {Note} on a {Prime} {Ring} with a {Maximal} {Annihilator} {Right} {Ideal}},
     journal = {Canadian mathematical bulletin},
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     year = {1965},
     volume = {8},
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     doi = {10.4153/CMB-1965-014-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-014-x/}
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