On the action of derivations on nilpotent ideals of associative algebras

• Date: 2009
• Main Authors: Luchko, V. S., Лучко, В. С.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3075
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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) o...