On the action of derivations on nilpotent ideals of associative algebras |
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Authors: | V. S. Luchko |
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Affiliation: | 1.Shevchenko Kiev National University,Kiev,Ukraine |
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Abstract: | 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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