Let M be a module and µ be a class of modules in Mod −R which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defnes a µ-essential submodule provided it has a non-zero intersection with any non-zero submodule in µ. We defne and investigate µ-singular modules. We also introduce µ-extending and weakly µ-extending modules and mainly study weakly µ-extending modules. We give some characterizations of µ-co-H-rings by weakly µ-extending modules. Let R be a right non-µ-singular ring such that all injective modules are non-µ-singular, then R is right µ-co-H-ring if and only if R is a QF-ring.
