Vol. 67, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 325: 1
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Vol. 319: 1  2
Vol. 318: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Rings whose proper cyclic modules are quasi-injective

Surender Kumar Jain, Surjeet Singh and Robin Gregory Symonds

Vol. 67 (1976), No. 2, 461–472
Abstract

A ring R with identity is a right PCQI-ring (PCI-ring) if every cyclic right R-module CR is quasi-injective (injective). Left PCQI-rings (PCI-rings) are similarly defined. Among others the following results are proved: (1) A right PCQI-ring is either prime or semi-perfect. (2) A nonprime nonlocal ring is a right PCQI-ring iff every cyclic right R-module is quasi-injective or R(D   D)
0   D , where D is a division ring. In particular, a nonprime nonlocal right PCQI-ring is also a left PCQI-ring. (3) A local right PCQI-ring with maximal ideal M is a right valuation ring or M2 = (0). (4) A prime local right PCQI-ring is a right valuation domain. (5) A right PCQI-domain is a right Öre-domain. Faith proved (5) for right PCI-domains. If R is commutative then some of the main results of Klatt and Levy on pre-self-injective rings follow as a special case of these results.

Mathematical Subject Classification
Primary: 16A52, 16A52
Milestones
Received: 19 November 1976
Published: 1 December 1976
Authors
Surender Kumar Jain
Surjeet Singh
Robin Gregory Symonds