Lie rings of derivations of associative rings

Jordan, C. R. and Jordan , D. A. (1978). Lie rings of derivations of associative rings. Journal of the London Mathematical Society, 2(17), pp. 33–41.

DOI (Digital Object Identifier) Link:	http://dx.doi.org/doi:10.1112/jlms/s2-17.1.33
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Abstract

Let $R$ be an associative ring with centre $Z$ . The aim of this paper is to study how the ideal structure of the Lie ring of derivations of $R$ , denoted $D(R)$ , is determined by the ideal structure of $R$ . If $R$ is a simple (respectively semisimple) finite-dimensional $Z$ -algebra and δ $(z)$ = 0 for all δ ∈ $D(R)$ , then every derivation of $R$ is inner and $D(R)$ is known to be a simple (respectively semisimple) Lie algebra (see [7, 5]). Here we are interested in extending these results to the case where $R$ is a prime or semi-prime ring.

Item Type:	Journal Article
Copyright Holders:	1978 London Mathematical Society
ISSN:	1469-7750
Extra Information:	MR number MR0472927
Academic Unit/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	31531
Depositing User:	Camilla Jordan
Date Deposited:	09 Feb 2012 12:34
Last Modified:	09 Feb 2012 12:34
URI:	http://oro.open.ac.uk/id/eprint/31531

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