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Higher commutators, ideals and cardinality

Published online by Cambridge University Press:  17 April 2009

Charles Lanski
Charles Lanski
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, United States of America, e-mail: clanski@ mtha.usc.edu
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Abstract

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For an associative ring R, we investigate the relation between the cardinality of the commutator [R, R], or of higher commutators such as [[R, R], [R, R]], the cardinality of the ideal it generates, and the index of the centre of R. For example, when R is a semiprime ring, any finite higher commutator generates a finite ideal, and if R is also 2-torsion free then there is a central ideal of R of finite index in R. With the same assumption on R, any infinite higher commutator T generates an ideal of cardinality at most 2cardT and there is a central ideal of R of index at most 2cardT in R.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 41 - 54
Copyright
Copyright © Australian Mathematical Society 1996

References

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