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
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 (36:209)
- [2] K. A. Brown and R. B. Warfield, Jr., Krull and global dimensions of fully bounded noetherian rings, Proc. Amer. Math. Soc. 92 (1984), 169-174. MR 754696 (86d:16019)
- [3] S. U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. MR 0120260 (22:11017)
- [4] I. Kaplansky, Fields and rings, Univ. of Chicago Press, Chicago, Ill., 1969. MR 0269449 (42:4345)
- [5] J. C. McConnell, On the global dimension of some rings, Math. Z. 153 (1977), 253-254. MR 0457498 (56:15703)
- [6] C. Procesi, Rings with polynomial identities, Dekker, New York, 1973. MR 0366968 (51:3214)
- [7]
R. Resco, L. W. Small and J. T. Stafford, Krull and global dimensions of semiprime noetherian
-rings, Trans. Amer. Math. Soc. 274 (1982), 285-295. MR 670932 (84g:16010)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A33, 16A38, 16A55, 16A60
Retrieve articles in all journals with MSC: 16A33, 16A38, 16A55, 16A60
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0754697-8
Keywords:
Noetherian ring,
polynomial identity,
Krull dimension,
homological dimension
Article copyright:
© Copyright 1984
American Mathematical Society