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A Note on Derivations of Group Rings

Published online by Cambridge University Press:  20 November 2018

Miguel Ferrero ,
Antonio Giambruno  and
César Polcino Milies
Miguel Ferrero
Affiliation:
Instituto de Matemática, Universidade Federal do Rio Grande do Sul, 91509-900 Porto Alegre, Brazil
Antonio Giambruno
Affiliation:
Dipartimento di Matematica, Universitá di Palermo Via Archirafi 34, 90123 Palermo, Italy
César Polcino Milies
Affiliation:
Instituto de Matemática e Estatistica, Universidade de São Paulo, Caixa postal 20.570, 01452-990 São Paulo, Brazil
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Abstract

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Let RG denote the group ring of a group G over a semiprime ring R. We prove that, if the center of G is of finite index and some natural restrictions hold, then every R-derivation of RG is inner. We also give an example of a group G which is both locally finite and nilpotent and such that, for every field F, there exists an F-derivation of FG which is not inner.

Keywords

16W2516S3416N60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 434 - 437
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Herstein, I. N., Non Commutative Rings, Cams Math. Monographs 15, 1968.Google Scholar
2. Smith, M. K., Derivations of Group Algebras of Finitely Generated Torsion-Free Nilpotent Groups, Houston J. Math. 4(1978), 277–288.Google Scholar