Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T03:37:15.556Z Has data issue: false hasContentIssue false
  • English
  • Français

A Result on Derivations with Algebraic Values

Published online by Cambridge University Press:  20 November 2018

Onofrio M. Di Vincenzo
Onofrio M. Di Vincenzo*
Affiliation:
Istituto Di Matematica Università Di Palermo Via 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.

Let R be a prime algebra over a field F and let d be a non-zero derivation in R such that for every x ∊ R, d(x) is algebraic over F of bounded degree. Then R is a primitive ring with a minimal right ideal eR, where e2 = e and eRe is a finite dimensional central division algebra.

Keywords

16A72
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 432 - 437
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Bergen, J., Ph.D. dissertation, U. of Chicago (1981).Google Scholar
2. Bergen, J., Lie ideals with regular and nilpotent elements and a result on derivations, Rend. Circ. Mat. Palermo (2). 33 (1984), pp. 99–108.Google Scholar
3. Herstein, I. N., Derivations of prime rings having power central values, Algebraists’ Homage, Contemporary Math. Vol. 13, AMS (1982). pp. 163-171.Google Scholar
4. Herstein, I. N., A note on derivations II, Can. Math. Bull., 22 (1979), pp. 509–511.Google Scholar
5. Herstein, I. N., A theorem on invariant subrings, J. Algebra, 83 (1983), pp. 26–32.Google Scholar
6. Herstein, I. N., Rings with involution, U. of Chicago Press (1976).Google Scholar