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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].

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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

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