Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-27T23:17:16.247Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bergen, J., Herstein, I. N. and Kerr, J. W. Lie ideals and derivations of prime rings, J. Algebra, 71 (1981), pp. 259–267.Google Scholar
2. Bergen, J., Herstein, I. N. and Lanski, C., Derivations with invertible values, Can. J. Math. 35 (1983), pp. 300–310.Google Scholar
3. Bergen, J., Lie ideals with regular and nilpotent elements and a result on derivations, Rend. Ci re. Mat. Palermo (2) 34 (1984), pp. 99–108.Google Scholar
4. Bergen, J., Carini, L., Derivations with invertible values on a Lie ideal, to appear.Google Scholar
5. Carini, L., Giambruno, A., Lie ideals and nil derivations, Boll. U.M.I. (6), 4-A (1985),pp. 497–503.Google Scholar
6. Herstein, I. N., Rings with involution, Univ. Chicago Press, Chicago, 1976.Google Scholar
7. Jacobson, N., Structure of rings, Amer. Math. Soc. Coll. Publ. 37 (1964).Google Scholar