Krull versus global dimension in Noetherian P.I. rings

Goodearl, K. R.; Small, L. W.

doi:10.1090/S0002-9939-1984-0754697-8

Krull versus global dimension in Noetherian P.I. rings

Authors: K. R. Goodearl and L. W. Small
Journal: Proc. Amer. Math. Soc. 92 (1984), 175-178
MSC: Primary 16A33; Secondary 16A38, 16A55, 16A60
DOI: https://doi.org/10.1090/S0002-9939-1984-0754697-8
MathSciNet review: 754697
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Krull dimension of any noetherian P.I. ring is bounded above by its global (homological) dimension (when finite).

[1] S. A. Amitsur, Prime rings having polynomial identities with arbitrary coefficients, Proc. London Math. Soc. (3) 17 (1967), 470–486. MR 0217118, https://doi.org/10.1112/plms/s3-17.3.470
[2] Kenneth A. Brown and R. B. Warfield Jr., Krull and global dimensions of fully bounded Noetherian rings, Proc. Amer. Math. Soc. 92 (1984), no. 2, 169–174. MR 754696, https://doi.org/10.1090/S0002-9939-1984-0754696-6
[3] Stephen U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457–473. MR 0120260, https://doi.org/10.1090/S0002-9947-1960-0120260-3
[4] Irving Kaplansky, Fields and rings, The University of Chicago Press, Chicago, Ill.-London, 1969. MR 0269449
[5] John C. McConnell, On the global dimension of some rings, Math. Z. 153 (1977), no. 3, 253–254. MR 0457498, https://doi.org/10.1007/BF01214478
[6] Claudio Procesi, Rings with polynomial identities, Marcel Dekker, Inc., New York, 1973. Pure and Applied Mathematics, 17. MR 0366968
[7] Richard Resco, Lance W. Small, and J. T. Stafford, Krull and global dimensions of semiprime Noetherian PI-rings, Trans. Amer. Math. Soc. 274 (1982), no. 1, 285–295. MR 670932, https://doi.org/10.1090/S0002-9947-1982-0670932-1