Given an injective envelope E of a left R-module M, there is an associative Galois group Gal($phi$). Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope E[$x^{-1}$] of an inverse polynomial module M[$x^{-1}$] as a left R[x]-module and we can define an associative Galois group Gal(${phi}[x^{-1}]$). In this paper we extend the Galois group of inverse polynomial module and can get Gal(${phi}[x^{-s}]$), where S is a submonoid of $mathds{N}$ (the set of all natural numbers).