Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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).


References [Enhancements On Off] (What's this?)

  • [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 $ PI$-rings, Trans. Amer. Math. Soc. 274 (1982), 285-295. MR 670932 (84g:16010)

Similar Articles

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

American Mathematical Society