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Derivations on a Lie Ideal

Published online by Cambridge University Press:  20 November 2018

Silvana Mauceri  and
Paola Misso
Silvana Mauceri
Affiliation:
Dlpartimento di Matematica ed Applicazioni, Università di PalermoVia Archirafi 34, 90123 Palermo, Italy
Paola Misso
Affiliation:
Dlpartimento di Matematica ed Applicazioni, Università di PalermoVia Archirafi 34, 90123 Palermo, Italy
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Abstract

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In this paper we prove the following result: let R be a prime ring with no non-zero nil left ideals whose characteristic is different from 2 and let U be a non central Lie ideal of R.

If d ≠ 0 is a derivation of R such that d(u) is invertible or nilpotent for all u ∈ U, then either R is a division ring or R is the 2 X 2 matrices over a division ring. Moreover in the last case if the division ring is non commutative, then d is an inner derivation of R.

Keywords

16A7216A12
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 3 , 01 September 1988 , pp. 280 - 286
Copyright
Copyright © Canadian Mathematical Society 1988

References

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