Geodesic
Radicals of Jordan rings connected with alternative rings
Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 135-140 
A. M. Slin'ko. Radicals of Jordan rings connected with alternative rings. Matematičeskie zametki, Tome 16 (1974) no. 1, pp. 135-140. http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a15/
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     author = {A. M. Slin'ko},
     title = {Radicals of {Jordan} rings connected with alternative rings},
     journal = {Matemati\v{c}eskie zametki},
     pages = {135--140},
     year = {1974},
     volume = {16},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_1_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Subject to a certain restriction on the additive group of an alternative ring $A$, we prove that $R(A)=R(A^{(+)})$, where $A^{(+)}$ is a Jordan ring and $R$ is one of the following radicals: the Jacobson radical, the upper nil-radical, the locally nilpotent radical, or the lower nil-radical. For the proof of these relationships Herstein's well-known construction for associative rings is generalized to alternative rings.