HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS
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In this note, we extend the Bre·sar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i)Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.
Abstract
In this note, we extend the Bre·sar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i)Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.
참고문헌 (5)
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- C. Haetinger, "Higher derivations on Lie ideals", Tendencias em Matematica Aplicada e Computacional, 3(1), pp.141~145 (2002)
- M. Ferrero, "Higher derivations and a theorem by Herstein", Quaestiones Mathematicae, 25(2), pp.249~257 (2002)
- M. Ferrero, "Higher derivations of semiprime rings", Communications in Algebra, 30(5), pp.2321~2333 (2002)
- P. Ribenboim, "Higher order derivations of modules", Portgaliae Math, 39, pp.381~397 (1980)