Vol. 85, No. 2, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 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
Injective hulls of group rings

Kenneth Alexander Brown and John William Lawrence

Vol. 85 (1979), No. 2, 323–343
Abstract

We are concerned in this paper with the following question: When is the maximal right quotient ring of the group algebra kG a right self-injective ring? In general, the maximal right quotient ring Q(R) of a ring R is a right R-submodule of the right injective hull E(R) of R, and we may rephrase our question as: When does Q(kG) = E(kG)? Of course, a sufficient condition for this to occur is that kG be right nonsingular, so that, for example, E(kG) = Q(kG) when k is a field of characteristic zero. However, Q(kG) is often injective even when kG is a singular ring; for example, when G is finite, it is well-known that kG is itself an injective ring.

Mathematical Subject Classification 2000
Primary: 20C07
Secondary: 16A27
Milestones
Received: 14 April 1978
Revised: 26 February 1979
Published: 1 December 1979
Authors
Kenneth Alexander Brown
John William Lawrence