On the action of derivations on nilpotent ideals of associative algebras
Let I be a nilpotent ideal of an associative algebra A over a field F and let D be a derivation of A. We prove that the ideal I + D(I) is nilpotent if char F = 0 or the nilpotency index I is less than char F = p in the case of the positive characteristic of the field F. In particular, the sum N(A) of all nilpotent ideals of the algebra A is a characteristic ideal if char F = 0 or N(A) is a nilpotent ideal of index < p = char F.
English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 7, pp 1187-1191.
Citation Example: Luchko V. S. On the action of derivations on nilpotent ideals of associative algebras // Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 1000-1004.