Pure projective modules and FP-injective modules over Morita rings

Let $${\Lambda _{(0,0)}} = \left( {\matrix{A \;\;\;\;\;\;\;\; {_A{N_B}} \cr {_B{M_A}}\;\;\;\; B \cr } } \right)$$ be a Morita ring, where the bimodule homomorphisms ϕ and ψ are zero. We study the finite presentedness, locally coherence, pure projectivity, pure injectivity, and FP-injectivity of modules over Λ(0,0). Some applications are then given.