# Article

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Keywords:
$\mu$-essential submodule; $\mu$-singular module; $\mu$-extending module; weakly $\mu$-extending module
Summary:
Let $M$ be a module and $\mu$ be a class of modules in $\operatorname{Mod}-R$ which is closed under isomorphisms and submodules. As a generalization of essential submodules Özcan in [8] defines a $\mu$-essential submodule provided it has a non-zero intersection with any non-zero submodule in $\mu$. We define and investigate $\mu$-singular modules. We also introduce $\mu$-extending and weakly $\mu$-extending modules and mainly study weakly $\mu$-extending modules. We give some characterizations of $\mu$-co-H-rings by weakly $\mu$-extending modules. Let $R$ be a right non-$\mu$-singular ring such that all injective modules are non-$\mu$-singular, then $R$ is right $\mu$-co-H-ring if and only if $R$ is a QF-ring.
References:
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