On weak injectivity and weak projectivity

Given a right R-module M, a module Q is an element of sigma [M] is said to be weakly injective in sigma [M] if for every finitely generated submodule N of the M-injective hull Q, N is contained in a submodule Y of Q ($) over cap such that Y similar or equal to Q. Weakly projective modules in sigma [M] are defined dually, Several characterizations of (weakly) semisimple modules are given in terms of tight and cotight modules in sigma [M].