Skew Injective Modules Relative to Torsion Theories

The purpose of this paper is to extend results about skew injective modules to a torsion theoretic setting. Given a hereditary torsion theory 𝜏 , a module 𝑀 is called 𝜏 -skew injective if all endomorphisms of 𝜏 -dense submodules of 𝑀 can be extended to endomorphismsof 𝑀 . A characterization of 𝜏 -skew injectivity using split short exact sequences is given.