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Semigroup identities on units of integral group rings

Published online by Cambridge University Press:  18 May 2009

Michael A. Dokuchaev  and
Jairo Z. Gonçalves
Michael A. Dokuchaev
Affiliation:
Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, CP 66281-AG Cid. de Sāo Paulo, CEP 05389-970 Sāo Paulo-Brazil, dokucha@ime.usp.br, jzg@ime.usp.br
Jairo Z. Gonçalves
Affiliation:
Instituto de Matemática e Estatistica, Universidade de Sāo Paulo, CP 66281-AG Cid. de Sāo Paulo, CEP 05389-970 Sāo Paulo-Brazil, dokucha@ime.usp.br, jzg@ime.usp.br
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Abstract

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Let U(RG) be the group of units of a group ring RG over a commutative ring R with 1. We say that a group is an SIT-group if it is an extension of a group which satisfies a semigroup identity by a torsion group. It is a consequence of the main result that if G is torsion and R = Z, then U(RG) is an SIT-group if and only if G is either abelian or a Hamiltonian 2-group. If R is a local ring of characteristic 0 only the first alternative can occur.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 1 , January 1997 , pp. 1 - 6
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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