Geodesic
A note on locally nilpotent rings with chain conditions
Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 121-126.

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It is shown that a locally nilpotent ring with maximality condition for two-sided ideals is nilpotent. The restriction on the characteristic in one of the author's previously published theorems is lifted. A one-sided nil-ideal of an alternative ring, satisfying the maximality condition for right ideals, is a nilpotent ring. An example is constructed of a commutative locally nilpotent ring $A$ with maximality condition for ideals which is idempotent: $A=A^2$. 
@article{MZM_1972_12_2_a0,
     author = {K. A. Zhevlakov},
     title = {A note on locally nilpotent rings with chain conditions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {121--126},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a0/}
}
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K. A. Zhevlakov. A note on locally nilpotent rings with chain conditions. Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 121-126. http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a0/