Pure projective modules and FP-injective modules over Morita rings

Let Λ(00)=(AANBBMAB)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Lambda _{(0,0)}} = \left( {\matrix{A \;\;\;\;\;\;\;\; {_A{N_B}} \cr {_B{M_A}}\;\;\;\; B \cr } } \right)$$\end{document} 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.