Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Krull and global dimensions of semiprime Noetherian PI-rings


Authors: Richard Resco, Lance W. Small and J. T. Stafford
Journal: Trans. Amer. Math. Soc. 274 (1982), 285-295
MSC: Primary 16A33; Secondary 16A38
MathSciNet review: 670932
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper it is shown that if $ R$ is a semiprime Noetherian PI-ring of finite global dimension, then the Krull dimension of $ R$ is less than or equal to its global dimension. The proof depends upon two preliminary results on arbitrary Noetherian PI-rings, which are of independent interest: (i) any height two prime ideal of $ R$ contains infinitely many height one prime ideals; (ii) the localization of the polynomial ring $ R[x]$ at its set of monic elements is a Jacobson ring.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A33, 16A38

Retrieve articles in all journals with MSC: 16A33, 16A38


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670932-1
PII: S 0002-9947(1982)0670932-1
Keywords: Noetherian PI-rings, Krull dimension, global dimension, Jacobson rings
Article copyright: © Copyright 1982 American Mathematical Society