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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

1. Bergen, J., Herstein, I. N. and C. Lanski, Derivations with invertible values, Can. J. Math. 35 (1983), pp. 300–310.Google Scholar
2. Brauer, R., On a theorem of H. Cartan, Bull. Amer. Math. Soc. 55 (1949), pp. 619–620.Google Scholar
3. Herstein, I. N., Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1959.Google Scholar
4. Herstein, I. N., A note on derivations, Can. Math. Bull. 21 (1978), pp. 369–370.Google Scholar
5. Herstein, I. N., A note on derivations II, Can. Math. Bull. 22 (1979), pp. 509–511.Google Scholar