\(\mathcal A\)-projective modules and the injective dimension of cyclic torsionless modules.
The author introduces and studies the concept of \(\mathcal A\)-projective module. Thus, a module \(M\) is called \(\mathcal A\)-projective if \(\text{Ext}^1_R(M,R/I)=0\) for any left annihilator \(I\) in \(R\). He also defines a dimension which measures how far away a ring is from being left self-injective von Neumann regular. Precisely, this left dimension of \(R\) is given as the supremum of all injective dimensions of cyclic torsionless left \(R\)-modules.
left self-injective von Neumann regular rings
scientific article; zbMATH DE number 5654590