Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T08:26:46.767Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

REFERENCES

1.Brown, K. A., The singular ideals of group rings, II, Quart. J. Math. Oxford Ser. 229, (1978), 187–197.CrossRefGoogle Scholar
2.Burgess, W. D., Rings of quotients of group rings; Canad. J. Math, 21 (1969), 865–875.CrossRefGoogle Scholar
3.Djoković, D. Ž. and Tang, C. Y., On the Frattini subgroup of the generalized free product with amalgamation, Proc. Amer. Math. Soc. 32 (1972), 21–23.CrossRefGoogle Scholar
4.Jordan, C. R., The Jacobson radical of the group ring of a generalised free product, J. London Math. Soc. (2) 11 (1975), 369–376.CrossRefGoogle Scholar
5.Jordan, C. R., Ph.D. Thesis, University of Leeds, 1975.Google Scholar
6.Lichtman, A. I., Ideals in group rings of free products with amalgamations and of HNN extensions, preprint.Google Scholar
7.Magnus, W., Karras, A. and Solitar, D., Combinatorial group theory (Interscience, 1966).Google Scholar
8.Neumann, B. H., An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503–554.Google Scholar
9.Passman, D. S., Infinite group rings (Marcel Dekker, 1971).Google Scholar