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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.
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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
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