1. Generalized derivations in prime and semiprime
- Author
-
Nadeem ur Rehman and Shuliang Huang
- Subjects
Discrete mathematics ,Mathematics::Commutative Algebra ,General Mathematics ,lcsh:Mathematics ,Semiprime ,Semiprime ring ,lcsh:QA1-939 ,Prime (order theory) ,generalized derivations ,GPIs ,Combinatorics ,Prime ring ,Ideal (ring theory) ,prime and semiprime rings ,Commutative property ,Mathematics - Abstract
Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$ is a semiprime ring.
- Published
- 2016