Almost QF rings with \(J^ 3=0\) (Q1327631)

The author has defined almost projective modules and almost injective modules [in J. Algebra 159, 150-157 (1993; Zbl 0795.16003)]. Let \(R\) be a two-sided artinian ring with identity. The author calls \(R\) a right almost QF ring in case \(R\) is almost injective as a right \(R\)-module. In this paper the author proves, among other things, that right almost QF rings are nothing but direct sums of serial rings and QF rings, provided \(J(R)^ 3 = 0\).