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Some examples of maximal orders

Published online by Cambridge University Press:  24 October 2008

P. F. Smith
P. F. Smith
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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In ([7], p. 181, problem 7) Maury and Raynaud pose the following question: ‘Let J be a ring and G a group such that the group ring J[G] is an order in a quotient ring Q; when is J[G] a maximal order in Q?’ The question is interesting for two reasons. In the first place, the analogous question for universal enveloping algebras of finite-dimensional Lie algebras has been settled very satisfactorily by Chamarie([2], corollaire 2·3·2). Secondly, it has been pointed out by several authors that maximal orders have some very desirable properties – see for example [3], [4], [6], [7] and [12].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 19 - 32
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REEFERENCES

[1]Brown, K. A.. Artinian quotient rings of group rings. J. Algebra 49 (1977), 63–80.CrossRefGoogle Scholar
[2]Chamarie, M.. Sur les ordres maximaux au sens d'asano. Vorlesungen aus dem Fachbereich Mathematik der Universität Essen Heft 3 (1979).Google Scholar
[3]Chamarie, M.. Anneaux de Krull non commutatif. J. Algebra 72 (1981), 210–222.CrossRefGoogle Scholar
[4]Chamarie, M.. Modules sur les anneaux de Krull non commutatif (Preprint.)Google Scholar
[5]Goldie, A. W.. The structure of prime rings under ascending chain conditions. Proc. London Math. Soc. (3) 8 (1958), 589–608.CrossRefGoogle Scholar
[6]Hajarnavis, C. R. and Robson, J. C.. Decomposition of maximal orders. Bull. London Math. Soc. 15 (1983), 123–125.CrossRefGoogle Scholar
[7]Maury, G. and Raynaud, J.. Ordres maximaux au sens de K. Asano. Springer Lecture Notes in Math. vol. 808 (1980).CrossRefGoogle Scholar
[8]Montgomery, S. and Passman, D. S.. Crossed products over prime rings. Israel J. Math. 31 (1978), 224–256.CrossRefGoogle Scholar
[9]Passman, D. S.. The algebraic structure of group rings (Wiley-Interscience, 1977).Google Scholar
[10] J.Roseblade, E.. Prime ideals in group rings of polycyclic groups. Proc. London Math. Soc. (3) 36 (1978), 385–447.Google Scholar
[11]Smith, P. F.. On the Intersection Theorem. Proc. London Math. Soc. (3) 21 (1970), 385–398.Google Scholar
[12]Stafford, J. T.. Modules over prime Krull rings (Preprint.)Google Scholar