Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-03T19:35:51.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Skew group rings and maximal orders

Published online by Cambridge University Press:  18 May 2009

R. Martin
R. Martin
Affiliation:
Department of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW
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 S be a prime Noetherian ring and G a finite group acting on 5 such that Gis x-outer on S. We give sufficient conditions for the skew group ring S * Gto be a prime maximal order. If we impose the further hypothesis that the order of Gbe a unit of S, then these conditions are also necessary. Moreover, if S is a commutative Noetherian domain, then there are necessary and sufficient conditions for S*Gto be a prime maximal order, without requiring that the order of G be a unit in S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 2 , May 1995 , pp. 249 - 263
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

REFERENCES

1.Chamarie, M., Anneaux de Krull non commutatifs, J. Algebra 72 (1981), 210–222.CrossRefGoogle Scholar
2.Cozzens, J. H. and Sandomierski, F. L., Maximal orders and localisation I, J. Algebra 44 (1987), 319–338.CrossRefGoogle Scholar
3.Eisenbud, D. and Robson, J. C., Hereditary Noetherian prime rings, J. Algebra 16 (1970), 86–104.CrossRefGoogle Scholar
4.Fuller, K. R. and Shutters, W. A., Projective modules over non-commutative semilocal rings, Tôhoku Math. J. (2) 27 (1975), 303–311.CrossRefGoogle Scholar
5.Goodearl, K. R. and Warfield, R. B. Jr, An introduction to noncommutative Noetherian rings, L. M. S. Student Texts 16 (C. U. P. 1989).Google Scholar
6.Hajarnavis, C. R. and Lenagan, T. H., Localisation in Asano orders, J. Algebra 21 (1972), 441–449.CrossRefGoogle Scholar
7.Hajarnavis, C. R. and Williams, S., Maximal orders in Artinian rings, J. Algebra 90 (1984), 375–384.CrossRefGoogle Scholar
8.McConnell, J. C. and Robson, J. C., Noncommutative Noetherian rings (Wiley-Interscience, 1987).Google Scholar
9.Martin, R., Skew group rings and maximal orders, Ph. D. Thesis, University of Glasgow (1993).Google Scholar
10.Maury, G. and Raynaud, J., Ordres maximaux au sens de K. Asano (Springer-Verlag, 1980).CrossRefGoogle Scholar
11.Müller, B. J., Localisation in fully bounded Noetherian rings, Pacific J. Math. 67 (1976), 233–245.CrossRefGoogle Scholar
12.Nauwelaerts, E. and Oystaeyen, F. van, Finitely generalised crossed products over tame and maximal orders, J. Algebra 101 (1986), 61–68.CrossRefGoogle Scholar
13.Passman, D. S., Infinite crossed products (Academic Press, 1989).Google Scholar
14.Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, 1977).Google Scholar
15.Reiner, I., Maximal orders (Academic Press, 1975).Google Scholar
16.Smith, P. F., Quotient rings of group rings, J. London Math. Soc. (2) 3 (1971), 645–660.CrossRefGoogle Scholar
17.Yi, Z., Homological dimension of skew group rings and crossed products, J. Algebra 164 (1994), 101–123.CrossRefGoogle Scholar