Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T01:04:46.024Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of maximal orders integral over their centres

Published online by Cambridge University Press:  18 May 2009

Andy J. Gray
Andy J. Gray
Affiliation:
Mathematics Institute, University Of Warwick, Coventry CV4 7AL.
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.

In a recent paper [1], Brown, Hajarnavis and MacEacharn have considered non-commutative Noetherian local rings of finite global dimension which are integral over their centres. For such a ring Rthey have shown:

(i) R is a prime ring whose Krull and global dimensions coincide;

(ii) R = ∩ RP where p runs through the set of rank one primes of the centre of R, and each Rp is hereditary;

(iii) the centre of R is a Krull domain.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 2 , July 1983 , pp. 177 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

REFERENCES

1.Brown, K. A., Hajarnavis, C. R. and MacEacharn, A. B., Rings of finite global dimension integral over their centres, Comm. Algebra, to appear.Google Scholar
2.Chamarie, M., Ordres maximaux et R-ordres maximaux, C.R. Acad. Sci. Paris Ser. A 285 (1977), 989–991.Google Scholar
3.Chamarie, M. and Hudry, A., Anneaux Noetheriéns à droit entiers sur un sous-anneau de leur centre, Comm. Algebra 6 (1978), 203–222.CrossRefGoogle Scholar
4.Chatters, A. W. and Hajarnavis, C. R., Rings with chain conditions (Pitman, London 1980).Google Scholar
5.Fossum, R. M., Maximal orders over Krull domains, J. Algebra 10 (1968), 321–332.CrossRefGoogle Scholar
6.Maury, G. and Raynaud, J., Ordres maximaux au sens de K. Asano, Lecture Notes in Mathematics 808 (Springer-Verlag, 1980).CrossRefGoogle Scholar
7.Vasconcelos, W., On quasi-local regular algebras, Symposia Mathematica1 11 (1973), 11–22.Google Scholar