Geodesic
Nilpotent Ideals in Alternative Rings
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 299-303

Voir la notice de l'article provenant de la source Cambridge University Press

It is well known and immediate that in an associative ring a nilpotent one-sided ideal generates a nilpotent two-sided ideal. The corresponding open question for alternative rings was raised by M. Slater [6, p. 476]. Hitherto the question has been answered only in the case of a trivial one-sided ideal J (i.e., in case J 2 = 0) [5]. In this note we solve the question in its entirety by showing that a nilpotent one-sided ideal K of an alternative ring generates a nilpotent two-sided ideal. In the process we find an upper bound for the index of nilpotency of the ideal generated. The main theorem provides another proof of the fact that a semiprime alternative ring contains no nilpotent one-sided ideals. Finally we note the analogous result for locally nilpotent one-sided ideals. 
Rich, Michael. Nilpotent Ideals in Alternative Rings. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 299-303. doi: 10.4153/CMB-1980-041-9
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