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Bull. Iranian Math. Soc
A module is said to be P I-extending provided that every projection invariant submodule is essential in a direct summand of the module. In this paper, we focus on direct summands and indecomposable decompositions of P I-extending modules. To this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper surfaces in projective spaces over complex numbers and obtain results when the P I-extending property isfatcat:buu2z22ozncbxpdxskwp6ircmy