Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-12-02T21:18:07.374Z Has data issue: false hasContentIssue false
  • English
  • Français

Some constructions of rings of finite global dimension

Published online by Cambridge University Press:  18 May 2009

J. C. Robson
J. C. Robson
Affiliation:
School of Mathematics, University of Leeds, Leeds, EnglandLS2 9JT
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 the study of idealizer rings in [14], the global dimensions of certain subrings were calculated. This work was extended by Goodearl [9]. Here it is shown, in Section 1, that the techniques involved can be used rather more generally than was apparent there. The results concern a ring S with a right ideal A such that SA = S, and a subring R of S containing A. They describe gl dim R in terms of gl dim S and the projective dimensions of simple subfactors of S/R or R/A, provided that these R-modules are sufficiently well conditioned.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 1 - 11
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

REFERENCES

1.Brown, K. A., Hajarnavis, C. R. and MacEacharn, A. B., Noetherian rings of finite global dimension, Proc. London Math. Soc. 44 (1982), 349–371.CrossRefGoogle Scholar
2.Brown, K. A., Hajarnavis, C. R. and MacEacharn, A. B., Rings of finite global dimension integral over their centres, Comm. Algebra, 11 (1983), 67–93.CrossRefGoogle Scholar
3.Brown, K. A. and Hajarnavis, C. R., Homologically homogeneous rings, Trans. Amer. Math. Soc. 281 (1984), 197–208.CrossRefGoogle Scholar
4.Chatters, A. W. and Hajarnavis, C. R., Rings with Chain Conditions (Pitman, 1980).Google Scholar
5.Eisenbud, D., Subrings of Artinian and Noetherian rings, Math. Ann. 185 (1970), 247–249.CrossRefGoogle Scholar
6.Eisenbud, D. and Robson, J. C., Modules over Dedekind prime rings, J. Algebra 16 (1970), 67–85.CrossRefGoogle Scholar
7.Fields, K. L., Examples of orders over discrete valuation rings, Math. Z. 111 (1969), 126–130.CrossRefGoogle Scholar
8.Formanek, E. and Jategaonkar, A. V., Subrings of Noetherian rings, Proc. Amer. Math. Soc. 46 (1974), 181–186.CrossRefGoogle Scholar
9.Goodearl, K. R., Subrings of idealizer rings, J. Algebra 33 (1975), 405–429.CrossRefGoogle Scholar
10.Jategaonkar, V. A., Global dimension of triangular orders over a discrete valuation ring, Proc. Amer. Math. Soc. 38 (1973), 8–14.CrossRefGoogle Scholar
11.Jategaonkar, V. A., Global dimension of tiled orders over commutative Noetherian domains, Trans. Amer. Math. Soc. 190 (1974), 357–374.CrossRefGoogle Scholar
12.Jategaonkar, V. A., Global dimension of tiled orders over a discrete valuation ring, Trans. Amer. Math. Soc. 196 (1974), 313–330.CrossRefGoogle Scholar
13.Levy, L. S., Torsionfree and divisible modules over non-integral domains, Canad. J. Math. 15 (1963), 132–151.CrossRefGoogle Scholar
14.Robson, J. C., Idealizers and hereditary Noetherian prime rings, J. Algebra 22 (1972), 45–81.CrossRefGoogle Scholar
15.Rowen, L. H., Polynomial Identities in Ring Theory(Academic Press, 1980).Google Scholar
16.Stafford, J. T. and Warfield, R. B., Constructions of hereditary Noetherian rings and simple rings, Proc. London Math. Soc., to appear.Google Scholar
17.Tarsy, R. B., Global dimension of orders, Trans. Amer. Math. Soc. 151 (1970), 335–340.CrossRefGoogle Scholar
18.Tarsy, R. B., Global dimension of triangular orders, Proc. Amer. Math. Soc. 28 (1971), 423–426.CrossRefGoogle Scholar
19.Vasconcelos, W. V., The Rings of Dimension Two (Dekker, 1976).Google Scholar