Almost QF rings and almost \(\text{QF}^ \#\) rings
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, and calls \(R\) a right almost \(\text{QF}^ \#\) ring in case every right injective \(R\)-module is almost projective. The main result states that \(R\) is right almost QF (almost \(\text{QF}^ \#\)) if and only if \(R\) is a right co-\(H\) ring (\(H\)-ring), i.e., every non-cosmall right \(R\)-module contains a projective direct summand (every non-small right \(R\)-module contains a non-zero injective module).
scientific article; zbMATH DE number 591444