IJPAM: Volume 25, No. 1 (2005)

SOME NOTES ON GENERALIZED LIE IDEALS

Neset Aydin$^1$, Öznur Gölbasi$^2$
$^1$Department of Mathematics
Faculty of Arts and Science
Çanakkale 18 Mart University
Çanakkale, 17020, TURKEY
e-mail: neseta@comu.edu.tr
$^2$Department of Mathematics
Cumhuriyet University
Sivas, 58140, TURKEY
e-mail: ogolbasi@cumhuriyet.edu.tr


Abstract.In [3], I.N. Herstein has proved if $R$ is a prime ring and $T
$ is a Lie ideal of $R$ such that $[T,T]\subset Z$ then $T\subset Z.$ In the first part of this note the above theorem is generalized for $(\sigma ,\tau
)-$left Lie ideal $U$ of prime ring. In the second part, some results given for one sided $(\sigma ,\tau
)-$left Lie ideals of prime rings.

Received: September 26, 2005

AMS Subject Classification: 16N60, 16W25, 16U80

Key Words and Phrases: Lie ideal, generalized Lie ideal, prime ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1