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] defines a μ-essential submodule provided it has a non-zero intersection with any non-zero submodule in μ. We define 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.
