Abstract
Relations between Goldie conditions of a semiprime algebraR and its subalgebraR d of constants under an algebraic derivation are studied. The results obtained are applied to actions of finite dimensional solvable Lie algebras on associative algebras with no non-zero nilpotent elements.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Bergen,Constants of Lie algebra actions, J. Algebra114 (1988), 452–465.
J. Bergen,Actions of solvable Lie algebras on rings with no nilpotent elements, J. Algebra135 (1990), 217–227.
J. Bergen and M. Cohen,Actions of commutative Hopf algebras, Bull. London Math. Soc.18 (1986), 159–164.
P. Grzeszczuk,On derivations of finite index. Chain conditions, dimensions and radicals, Israel J. Math.58 (1987), 54–66.
P. Grzeszczuk,On nilpotent derivations of semiprime rings, J. Algebra149 (1992), 313–321.
P. Grzeszczuk,Constants of algebraic derivations, Comm. Algebra (to appear).
V.K. Kharchenko,Constants of derivations of prime rings, Izv. Akad. Nauk. SSSR, Ser. Matem45 (1981), 435–447; English transl. Math. USSR Izv.18 (1982), 381–400.
A.Z. Popov,Derivations of prime rings, Algebra i Logika22 (1983), 79–92.
Author information
Authors and Affiliations
Additional information
Supported by KBN Grant No. 2 2012 91 02.
Supported by KBN Grant No. 2 2047 91 02.
Rights and permissions
About this article
Cite this article
Grzeszczuk, P., Matczuk, J. Goldie conditions for constants of algebraic derivations of semiprime algebras. Israel J. Math. 83, 329–342 (1993). https://doi.org/10.1007/BF02784060
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02784060