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Ideals in simple rings

Published online by Cambridge University Press:  09 April 2009

W. Harold Davenport
W. Harold Davenport
Affiliation:
Department of Mathematics, University of Petroleum & Minerals, Dhahran, Saudi Arabia.
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Abstract

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In this article, we define the concept of a Malcev ideal in an alternative ring in a manner analogous to Lie ideals in associative rings. By using a result of Kleinfield's we show that a nonassociative alternative ring of characteristic not 2 or 3 is a ring sum of Malcev ideals Z and [R, R] where Z is the center of R and [R, R] is a simple non-Lie Malcev ideal of R. If R is a Cayley algebra over a field F of characteristic 3 then [R, R] is a simple 7 dimensional Lie algebra. A similar result is obtained if R is a simple associative ring.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 322 - 327
Copyright
Copyright © Australian Mathematical Society 1978

References

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