Geodesic
Some constructions of rings of finite global dimension
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 1-11

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Robson, J. C. Some constructions of rings of finite global dimension. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 1-11. doi: 10.1017/S001708950000570X
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[1] 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. Google Scholar | DOI

[2] 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. Google Scholar | DOI

[3] 3.Brown, K. A. and Hajarnavis, C. R., Homologically homogeneous rings, Trans. Amer. Math. Soc. 281 (1984), 197–208. Google Scholar | DOI

[4] 4.Chatters, A. W. and Hajarnavis, C. R., Rings with Chain Conditions (Pitman, 1980). Google Scholar

[5] 5.Eisenbud, D., Subrings of Artinian and Noetherian rings, Math. Ann. 185 (1970), 247–249. Google Scholar | DOI

[6] 6.Eisenbud, D. and Robson, J. C., Modules over Dedekind prime rings, J. Algebra 16 (1970), 67–85. Google Scholar | DOI

[7] 7.Fields, K. L., Examples of orders over discrete valuation rings, Math. Z. 111 (1969), 126–130. Google Scholar | DOI

[8] 8.Formanek, E. and Jategaonkar, A. V., Subrings of Noetherian rings, Proc. Amer. Math. Soc. 46 (1974), 181–186. Google Scholar | DOI

[9] 9.Goodearl, K. R., Subrings of idealizer rings, J. Algebra 33 (1975), 405–429. Google Scholar | DOI

[10] 10.Jategaonkar, V. A., Global dimension of triangular orders over a discrete valuation ring, Proc. Amer. Math. Soc. 38 (1973), 8–14. Google Scholar | DOI

[11] 11.Jategaonkar, V. A., Global dimension of tiled orders over commutative Noetherian domains, Trans. Amer. Math. Soc. 190 (1974), 357–374. Google Scholar | DOI

[12] 12.Jategaonkar, V. A., Global dimension of tiled orders over a discrete valuation ring, Trans. Amer. Math. Soc. 196 (1974), 313–330. Google Scholar | DOI

[13] 13.Levy, L. S., Torsionfree and divisible modules over non-integral domains, Canad. J. Math. 15 (1963), 132–151. Google Scholar | DOI

[14] 14.Robson, J. C., Idealizers and hereditary Noetherian prime rings, J. Algebra 22 (1972), 45–81. Google Scholar | DOI

[15] 15.Rowen, L. H., Polynomial Identities in Ring Theory(Academic Press, 1980). Google Scholar

[16] 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] 17.Tarsy, R. B., Global dimension of orders, Trans. Amer. Math. Soc. 151 (1970), 335–340. Google Scholar | DOI

[18] 18.Tarsy, R. B., Global dimension of triangular orders, Proc. Amer. Math. Soc. 28 (1971), 423–426. Google Scholar | DOI

[19] 19.Vasconcelos, W. V., The Rings of Dimension Two (Dekker, 1976). Google Scholar

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