Vol. 85, No. 2, 1979

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Injective hulls of group rings

Kenneth Alexander Brown and John William Lawrence

Vol. 85 (1979), No. 2, 323–343

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
Received: 14 April 1978
Revised: 26 February 1979
Published: 1 December 1979
Kenneth Alexander Brown
John William Lawrence