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Derivations with Invertible Values on a Lie Ideal

Published online by Cambridge University Press:  20 November 2018

Jeffrey Bergen  and
L. Carini
Jeffrey Bergen
Affiliation:
Depaul University, ChicagoIL 60614 USA
L. Carini
Affiliation:
Dlpartimento dl Matematica, Dell UniversitàVia C. Battisti 90, 98100 Messina, Italy
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Abstract

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Let R be a ring which possesses a unit element, a Lie ideal U ⊄ Z, and a derivation d such that d(U) ≠ 0 and d(u) is 0 or invertible, for all u ∈ U. We prove that R must be either a division ring D or D2, the 2 X 2 matrices over a division ring unless d is not inner, R is not semiprime, and either 2R or 3R is 0. We also examine for which division rings D, D2 can possess such a derivation and study when this derivation must be inner.

Keywords

16A6816A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 103 - 110
Copyright
Copyright © Canadian Mathematical Society 1988

References

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