A module is said to be π-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this article, we focus on the class of modules having the π-extending property by looking at the singularity of quotient submodules. By doing so, we provide counterexamples, using hypersurfaces in projective spaces over complex numbers, to show that being generalized π-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized π-extending modules are generalized π-extending.

Keywords: extending modules, π-extending module, projection invariant.