Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Lie solvable rings


Authors: R. K. Sharma and J. B. Srivastava
Journal: Proc. Amer. Math. Soc. 94 (1985), 1-8
MSC: Primary 16A68
DOI: https://doi.org/10.1090/S0002-9939-1985-0781044-9
MathSciNet review: 781044
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathcal {L}(R)$ denote the associated Lie ring of an associative ring $R$ with identity $1 \ne 0$ under the Lie multiplication $[x,y] = xy - yx$ with $x,y \in R$. Further, suppose that the Lie ring $\mathcal {L}(R)$ is solvable of length $n$. It has been proved that if 3 is invertible in $R$, then the ideal $J$ of $R$ generated by all elements $[[[{x_1},{x_2}],[{x_3},{x_4}]],{x_5}],\;{x_1},\;{x_2},\;{x_3},\;{x_4},\;{x_5} \in R$, is nilpotent of index at most $\tfrac {2}{9}(19 \cdot {10^{n - 3}} - 1)$ for $n \geqslant 3$. Also, if 2 and 3 are both invertible in $R$, then the ideal $I$ of $R$ generated by all elements $[x,y],\;x,y \in R$, is a nil ideal of $R$. Some applications to Lie solvable group rings are also given.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A68

Retrieve articles in all journals with MSC: 16A68


Additional Information

Keywords: Lie solvable ring, associated Lie ring
Article copyright: © Copyright 1985 American Mathematical Society