Vol. 69, No. 2, 1977

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Classes of rings torsion-free over their centers

Louis Halle Rowen

Vol. 69 (1977), No. 2, 527–534
Abstract

Let J( ) denote the intersection of the maximals ideals of a ring. The following properties are studied, for a ring R torsion-free over its center C: (i) J(R) C = J(C); (ii) “Going up” from prime ideals of C to prime ideals of R; (iii) If M is a maximal ideal of R then M C is a maximal ideal of C; (iv) if M is a maximal (resp. prime) ideal of C, then M = MR C. Properties (i)–(iv) are known to hold for many classes of rings, including rings integral over their centers or finite modules over their centers. However, using an idea of Cauchon, we show that each of (i)–(iv) has a counterexample in the class of prime Noetherian PI-rings.

Mathematical Subject Classification
Primary: 16A48, 16A48
Milestones
Received: 12 March 1976
Published: 1 April 1977
Authors
Louis Halle Rowen
Bar Ilan University
Ramat Gan
Israel