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On the group ring of a free product with amalgamation

Published online by Cambridge University Press:  18 May 2009

Camilla R. Jordan
Camilla R. Jordan
Affiliation:
c/o Dr. D. A. Jordan, Department of Pure Mathematics, The University of Sheffield, The Hicks Building, Sheffield S3 7RH
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Let G = A*HB be the free product of the groups A and B amalgamating the proper subgroup H and let R be a ring with 1. If H is finite and G is not finitely generated we show that any non-zero ideal I of R(G) intersects non-trivially with the group ring R(M), where M = M(I) is a subgroup of G which is a free product amalgamating a finite normal subgroup. This result compares with A. I. Lichtman's results in [6] but is not a direct generalisation of these.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 135 - 138
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

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