Tercan, Adnan2024-11-062024-11-062019-09-011225-6951https://doi.org/10.5666/KMJ.2019.59.3.391https://hdl.handle.net/11452/47499A module is said to be pi-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 pi-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 pi-extending is not inherited by direct summands. Moreover, it is shown that the direct sums of generalized pi-extending modules are generalized pi-extending.eninfo:eu-repo/semantics/closedAccessModulesExtending modulesPi-extending moduleProjection invariantScience & technologyPhysical sciencesMathematicsArticle00048910630000339140159310.5666/KMJ.2019.59.3.391