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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Homologically homogeneous rings


Authors: K. A. Brown and C. R. Hajarnavis
Journal: Trans. Amer. Math. Soc. 281 (1984), 197-208
MSC: Primary 16A60; Secondary 16A33
DOI: https://doi.org/10.1090/S0002-9947-1984-0719665-5
MathSciNet review: 719665
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Abstract: In this paper we study the structure of a right Noetherian ring $ R$ of finite right global dimesion integral over a central subring $ C$ and satisfying the following condition:

if $ V,W$ are irreducible right $ R$-modules with $ {r_C}(V) = {r_C}(W)$ then $ \operatorname{pr}\, \dim (V) = \operatorname{pr}\, \dim (W)$.


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  • [1] G. M. Bergman and P. M. Cohn, The centres of $ 2$-firs and hereditary rings, Proc. London Math. Soc. 23 (1971), 83-98. MR 0291200 (45:294)
  • [2] J. Bernstein, I. Gelfand and S. Gelfand, Structure locale de la catégorie des modules de Harish-Chandra, C. R. Acad. Sci. Paris 286 (1978), 495-497. MR 489155 (81e:22026)
  • [3] S. M. Bhatwadekar, On the global dimension of some filtered algebras, J. London Math. Soc. (2) 13 (1976), 239-248. MR 0404398 (53:8200)
  • [4] K. A. Brown, C. R. Hajarnavis and A. B. MacEacharn, Noetherian rings of finite global dimension, Proc. London Math. Soc. 44 (1982), 349-371. MR 647437 (84a:16025)
  • [5] -, Rings of finite global dimension integral over their centers, Comm. Algebra 11 (1983), 67-93. MR 687406 (84b:16029)
  • [6] M. Chamarie, Localisations dans les ordres maximaux, Comm. Algebra 2 (1974), 279-293. MR 0352154 (50:4641)
  • [7] M. Chamarie and A. Hudry, Anneaux noethériens à droite entiers sur un sous-anneau de leur centre, Comm. Algebra 6 (1978), 203-222. MR 0463241 (57:3194)
  • [8] A. W. Chatters and C. R. Hajarnavis, Rings with chain conditions, Pitman, London, 1980. MR 590045 (82k:16020)
  • [9] R. Gordon and J. C. Robson, Krull dimension, Mem. Amer. Math. Soc., no. 133, 1973. MR 0352177 (50:4664)
  • [10] A. Gray, A class of maximal orders integral over their centres, Glasgow Math. J. (to appear). MR 706147 (84m:16010)
  • [11] S. Jøndrup, Homological dimensions of some $ P.\ I.$ rings, Comm. Algebra 8 (1980), 685-696. MR 561548 (82f:16013)
  • [12] I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 0254021 (40:7234)
  • [13] D. S. Passman, The algebraic structure of group rings, Interscience, New York, 1977. MR 470211 (81d:16001)
  • [14] R. Resco, L. W. Small and J. T. Stafford, Krull and global dimensions of semiprime Noetherian $ PI$-rings, Trans. Amer. Math. Soc. 274 (1982), 285-295. MR 670932 (84g:16010)
  • [15] J. C. Robson, Some constructions of rings of finite global dimension (to appear). MR 776670 (86i:16026)
  • [16] J. J. Rotman, An introduction to homological algebra, Academic Press, New York, 1979. MR 538169 (80k:18001)
  • [17] L. H. Rowen, Polynomial identities in ring theory, Academic Press, New York, 1980. MR 576061 (82a:16021)
  • [18] B. Stenström, Rings of quotients, Springer-Verlag, Berlin and New York, 1975. MR 0389953 (52:10782)
  • [19] R. G. Swan, Groups of cohomological dimension one, J. Algebra 12 (1969), 585-610. MR 0240177 (39:1531)
  • [20] R. B. Tarsy, Global dimension of orders, Trans. Amer. Math. Soc. 151 (1970), 335-340. MR 0268226 (42:3125)
  • [21] V. W. Vasconcelos, On quasi-local regular algebras, Symposia Math., Vol. XI, Academic Press, London, 1973. MR 0330159 (48:8497)

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DOI: https://doi.org/10.1090/S0002-9947-1984-0719665-5
Article copyright: © Copyright 1984 American Mathematical Society

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