Derivations on prime and semi-prime rings
Bull. Korean Math. Soc. 2002 Vol. 39, No. 3, 485-494
Printed September 1, 2002
Eun Hwi Lee, Yong-Soo Jung, and Ick-Soon Chang
Jeonju University, Chungnam National University, Chungnam National University
Abstract : In this paper we will show that if there exist derivations $D$, $G$ on a $n!$-torsion free semi-prime ring $R$ such that the mapping $D^{2}+G$ is n-commuting on $R$, then $D$ and $G$ are both commuting on $R$. And we shall give the algebraic conditions on a ring that a Jordan derivation is zero.
Keywords : torsion free ring, derivation, commuting, $n$-commuting, Jordan derivation, prime, semi-prime, semisimple, noncommutative Banach algebras
MSC numbers : 16A12, 16A70, 16A72, 46H40, 46J10, 47B47
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