Hostname: page-component-5c6d5d7d68-thh2z Total loading time: 0 Render date: 2024-08-18T19:27:59.443Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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