Pure projective modules and FP-injective modules over Morita rings (Q2035151)

The authors study several properties about a Morita ring \(\Lambda\) where bimodule homomorphisms are zero. The authors describe when a \(\Lambda\)-module is finitely presented (Prop 3.2, 3.3 and Thm 3.12), pure projective (Prop 4.6), pure injective (Prop 4.7), locally coherent (Prop 5.3), (strongly) FP-injective (Lemma 6.6). Finally, in Prop 5.6 they give an equivalent condition for \(\Lambda\) to be a left J-coherent ring, or (Cor 6.10) to be an FC ring.