Geodesic
One-sided nil-ideals and generalized polynomial identities of semi-prime rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 809-811.

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In the paper it is shown that semi-prime rings (rings with strong identities) have no one-sided ideals with Gardner's property (r) [1] (respectively, no non-zero one-sided nil-ideals). 
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Yu. A. Terekhova. One-sided nil-ideals and generalized polynomial identities of semi-prime rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 3, pp. 809-811. http://geodesic.mathdoc.fr/item/FPM_1995_1_3_a16/

[1] B. J. Gardner, “Some nil rings properties related to T-nilpotence”, Bull. Austral. Math. Soc., 46 (1992), 519–523 | DOI | MR | Zbl

[2] Wallace S. Martindale, “Prime rings satisfying a generalized polynomial identity”, J. Algebra, 12 (1969), 576–584 | DOI | MR | Zbl

[3] I. N. Herstein, Topics in ring theory, Univ. Chicago Press, Chicago, 1969 | MR | Zbl

[4] I. Lambek, Koltsa i moduli, Mir, M., 1971 | MR | Zbl

[5] K. I. Beidar, “Koltsa s obobschennymi tozhdestvami II”, Vestnik Mosk. un-ta. Matem., mekhan., 1977, 3

[6] K. I. Beidar, “Koltsa s obobschennymi tozhdestvami IV”, Vestnik Mosk. un-ta. Matem., mekhan., 1980, 4

[7] K. I. Beidar, Koltsa s obobschennymi tozhdestvami:, Dis. ... kand. fiz.-mat. nauk, M., 1977