DERIVATIONS ON PRIME AND SEMI-PRIME RINGS

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

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References

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Cited by

1. Generalized Derivations and Commuting Additive Maps on Multilinear Polynomials in Prime Rings vol.68, pp.2, 2016, https://doi.org/10.1007/s11253-016-1219-0
2. On n-commuting and n-skew-commuting maps with generalized derivations in prime and semiprime rings vol.52, pp.3, 2011, https://doi.org/10.1134/S0037446611030141