Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T15:43:01.397Z Has data issue: false hasContentIssue false
  • English
  • Français

On the automorphisms of the group ring of a finitely generated free abelian group

Published online by Cambridge University Press:  20 January 2009

M. M. Parmenter
M. M. Parmenter
Affiliation:
Department of Mathematics and StatisticsMemorial University of NewfoundlandSt John'sNewfoundlandCanadaA1B 3X7
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 R be an associative ring with 1 and G a finitely generated torsion-free abelian group. In this note, we classify all R-automorphisms of the group ring RG. The special case where G is infinite cyclic was previously settled in [8], and our interest in this problem was rekindled by the recent paper of Mehrvarz and Wallace [7], who carried out the classification in the case where R contains a nilpotent prime ideal.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 1 , February 1988 , pp. 71 - 75
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Bass, Hyman, Automorphisms of Polynomial Rings, Abelian Group Theory (Springer Lecture Notes 1006, Springer-Verlag, Berlin-New York, 1983), 762–771.Google Scholar
2.Cohn, P. M., Free Rings and their Relations, second edition (Academic Press, 1985).Google Scholar
3.Coleman, D. B. and Enochs, E. E., Isomorphic polynomial rings, Proc. Amer. Math. Soc. 27 (1971), 247–252.Google Scholar
4.Dicks, Warren, Automorphisms of the polynomial ring in two variables, Pub. Mat. U AB 27 (1983), 155–162.Google Scholar
5.Gilmer, R. W. Jr., R-automorphisms of R[x], Proc. London Math. Soc. 18 (1968), 328–336.Google Scholar
6.Lantz, David C., R-automorphisms of R[G] for G abelian torsion-free, Proc. Amer. Math. Soc. 61 (1976), 1–6.Google Scholar
7.Mehrvarz, A. A. and Wallace, D. A. R., On the automorphisms of the group ring of a unique product group, Proc. Edinburgh Math. Soc., to appear.Google Scholar
8.Parmenter, M. M., Isomorphic group rings, Canad. Math. Bull. 18 (1975), 567–576.Google Scholar
9.Parmenter, M. M., Units and isomorphism in group rings, Quaest. Math. 8 (1985), 9–14.Google Scholar
10.Sehgal, S. K., Topics in Group Rings (Marcel Dekker, New York, 1978).Google Scholar