On almost M-projectives and almost M-injectives (Q2639935)

Almost M-injectivity and almost M-projectivity was defined by the authors respectively in earlier papers as generalizations of the well-known concepts of M-injectivity and M-projectivity. Necessary and sufficient conditions for a direct sum of certain sets of modules to be a lifting module are found in terms of the almost M-projectivity of the summands and also in terms of the lifting property of direct summands modulo submodules. A characterization of lifting modules over a right artinian ring completes the part on almost M-projectives and the paper is concluded by two sections studying dual properties of M-injectives.