Abstract
We show that if perspectivity is transitive in a Utumi-module M, then E(M) satisfies the substitution property. Moreover, we also prove that if M is either a quasi-continuous or an auto-invariant module, then M is perspective if and only if E(M) is perspective. As an immediate consequence, we recover a result of Khurana and Nielsen, by proving that if perspectivity is transitive in a quasi-continuous module M, then both M and E(M) are perspective modules. The later result also extends the work of Amini, Amini and Momtahan on quasi-injective modules.