On the action of derivations on nilpotent ideals of associative algebras
AbstractLet 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.
How to Cite
Luchko, V. S. “On the Action of Derivations on Nilpotent Ideals of Associative Algebras”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 7, July 2009, pp. 1000-4, https://umj.imath.kiev.ua/index.php/umj/article/view/3075.