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Dependent Automorphisms in Prime Rings

Published online by Cambridge University Press:  20 November 2018

Matej Brešar ,
W. S. Martindale 3rd  and
C. Robert Miers
Matej Brešar
Affiliation:
University of Maribor PF, Koroška 160 62000 Maribor Slovenia
W. S. Martindale 3rd
Affiliation:
Department of Mathematics University of Massachusetts Amherst, MA 01003 USA
C. Robert Miers
Affiliation:
Department of Mathematics and Statistics University of Victoria Victoria, BC V8W 3P4
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Abstract

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For each $n\ge 4$ we construct a class of examples of a minimal $C$-dependent set of $n$ automorphisms of a prime ring $R$, where $C$ is the extended centroid of $R$. For $n=4$ and $n=5$ it is shown that the preceding examples are completely general, whereas for $n=6$ an example is given which fails to enjoy any of the nice properties of the above example.

Keywords

16N6016W20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 452 - 462
Copyright
Copyright © Canadian Mathematical Society 1998

References

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[C] Brešar, M., On certain pairs of automorphisms of rings, II. Preprint.Google Scholar
[D] Martindale, W. S. III and Susan Montgomery, The normal closure of coproducts of domains. J. Algebra 82 (1983), 1–17.Google Scholar