In this paper we introduce the concept of τ -extending modules by τ - rational submodules and study some properties of such modules. It is shown that the set of all τ -rational left ideals of R R is a Gabriel filter. An R-module M is called τ -extending if every submodule of M is τ -rational in a direct summand of M . It is proved that M is τ -extending if and only if M = RejM E(R/τ (R))⊕N , such that N is a τ -extending submodule of M . An example is given to show that the direct sum of τ -extending modules need not be τ -extending.
