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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 7, pp. 1000–1004, July, 2009.
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Luchko, V.S. On the action of derivations on nilpotent ideals of associative algebras. Ukr Math J 61, 1187–1191 (2009). https://doi.org/10.1007/s11253-009-0259-0
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DOI: https://doi.org/10.1007/s11253-009-0259-0